Information processing at the speed of light.

AbuGhanem, M., Eleuch, H.: NISQ Computers: a path to quantum supremacy. IEEE Access 12, 102941–102961 (2024)

doi: 10.1109/ACCESS.2024.3432330

DiVincenzo, D.: The physical implementation of quantum computation. Fortschr. Phys. 48, 9–11 (2000)

doi: 10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E

DiVincenzo, D., Bacon, D., Kempe, J., Burkard, G., Whaley, K.B.: Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)

doi: 10.1038/35042541

DeMille, D.: Quantum computation with trapped polar molecules. Phys. Rev. Lett. 88, 067901 (2002)

doi: 10.1103/PhysRevLett.88.067901

Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312 (2003)

doi: 10.1103/PhysRevA.68.022312

Vidal, G.: Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003)

doi: 10.1103/PhysRevLett.91.147902

Blais, A., Huang, R.S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

doi: 10.1103/PhysRevA.69.062320

Walther, P., Resch, K., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., Zeilinger, A.: Experimental one-way quantum computing. Nature 434, 169–176 (2005)

doi: 10.1038/nature03347

Sørensen, A., Mølmer, K.: Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82, 1971 (1999)

doi: 10.1103/PhysRevLett.82.1971

Braunstein, S.L., Caves, C.M., Jozsa, R., Linden, N., Popescu, S., Schack, R.: Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett. 83, 1054 (1999)

doi: 10.1103/PhysRevLett.83.1054

Zanardi, P., Rasetti, M.: Holonomic quantum computation. Phys. Lett. A 264, 2–3 (1999)

doi: 10.1016/S0375-9601(99)00803-8

Vrijen, R., Yablonovitch, E., Wang, K., Jiang, H.W., Balandin, A., Roychowdhury, V., Mor, T., DiVincenzo, D.: Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures. Phys. Rev. A 62, 012306 (2000)

doi: 10.1103/PhysRevA.62.012306

Ioffe, L., Geshkenbein, V., Feigel’man, M., Fauchère, A.L., Blatter, G.: Environmentally decoupled [Formula: see text]-wave Josephson junctions for quantum computing. Nature 398, 679–681 (1999)

doi: 10.1038/19464

Kielpinski, D., Monroe, C., Wineland, D.: Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002)

doi: 10.1038/nature00784

Jones, J., Vedral, V., Ekert, A., Castagnoli, G.: Geometric quantum computation using nuclear magnetic resonance. Nature 403, 869–871 (2000)

doi: 10.1038/35002528

Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)

doi: 10.1103/PhysRevLett.86.5188

Leuenberger, M., Loss, D.: Quantum computing in molecular magnets. Nature 410, 789–793 (2001)

doi: 10.1038/35071024

Knill, E., Laflamme, R., Milburn, G.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)

doi: 10.1038/35051009

Kitaev, A.Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 203, 2–3 (2003)

doi: 10.1016/S0003-4916(02)00018-0

Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457 (1995)

doi: 10.1103/PhysRevA.52.3457

AbuGhanem, M., Eleuch, H.: Experimental characterization of Google’s Sycamore quantum AI on an IBM’s quantum computer, Elsevier, SSRN 4299338 (2023)

AbuGhanem, M., Eleuch, H.: Full quantum tomography study of Google’s Sycamore gate on IBM’s quantum computers. EPJ Quantum Technol. 11(1), 36 (2024)

doi: 10.1140/epjqt/s40507-024-00248-8

DiVincenzo, D.P.: Quantum computation. Science 270, 5234 (1995)

doi: 10.1126/science.270.5234.255

Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45 (2010)

doi: 10.1038/nature08812

Nielsen, M. A., Chuang, I. L.: Quantum Computation and Quantum Information. 10th anniversary ed., Cambridge University Press (2011)

Scholten, T. L., Williams, C. J., Moody, D., Mosca, M., Hurley, W., Zeng, W. J., Troyer, M., Gambetta, J.M.: Assessing the benefits and risks of quantum computers. arXive preprints arXiv:2401.16317 [quant-ph] (2024)

Feynman, R.P.: Feynman and Computation. Simulating Physics with Computers. pp. 133–153. Routledge, New York (2018)

doi: 10.1201/9780429500459-11

Benioff, P.: The computer as a physical system: a microscopic quantum mechanical hamiltonian model of computers as represented by turing machines. J. Stat. Phys. 22(5), 563–591 (1980)

doi: 10.1007/BF01011339

Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A Math. Phys. Sci. 439(1907), 553–558 (1992)

Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. A Math. Phys. Sci. 400(1818), 97–117 (1985)

Bernstein, E., Vazirani, U.: Quantum complexity theory. SIAM J. Comput. 26(5), 1411–1473 (1997)

doi: 10.1137/S0097539796300921

Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997)

doi: 10.1137/S0097539796298637

Harrow, A.W., Montanaro, A.: Quantum computational supremacy. Nature 549(7671), 203–209 (2017)

doi: 10.1038/nature23458

Ralph, T., Pryde, G.: Optical quantum computation. Prog. Opt. 54, 209–269 (2010)

doi: 10.1016/S0079-6638(10)05409-0

Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007)

doi: 10.1103/RevModPhys.79.135

Obrien, J.L., Furusawa, A., Vuckovic, J.: Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009)

doi: 10.1038/nphoton.2009.229

Takeda, S., Furusawa, A.: Toward large-scale fault-tolerant universal photonic quantum computing. APL Photonics 4, 060902 (2019)

doi: 10.1063/1.5100160

Obrien, J.L.: Optical quantum computing. Science 318(5856), 1567–1570 (2007)

doi: 10.1126/science.1142892

Flamini, F., Spagnolo, N., Sciarrino, F.: Photonic quantum information processing: a review. Rep. Prog. Phys. 82, 016001 (2018)

doi: 10.1088/1361-6633/aad5b2

Slussarenko, S., Pryde, G.J.: Photonic quantum information processing: a concise review. Appl. Phys. Rev. 6(4), 041303 (2019)

doi: 10.1063/1.5115814

Liao, S.K., Cai, W.Q., Liu, W.Y., Zhang, L., Li, Y., Ren, J.G., Yin, J., Shen, Q., Cao, Y., Li, Z.P., Li, F.Z., Chen, X.W., Sun, L.H., Jia, J.J., Wu, J.C., Jiang, X.J., Wang, J.F., Huang, Y.M., Wang, Q., Zhou, Y.L., Deng, L., Xi, T., Ma, L., Hu, T., Zhang, Q., Chen, Y.A., Liu, N.L., Wang, X.B., Zhu, Z.C., Lu, C.Y., Shu, R., Peng, C.Z., Wang, J.Y., Pan, J.W.: Satellite-to-ground quantum key distribution. Nature 549(7670), 43–47 (2017)

doi: 10.1038/nature23655

Ren, J.G., Xu, P., Yong, H.L., Zhang, L., Liao, S.K., Yin, J., Liu, W.Y., Cai, W.Q., Yang, M., Li, L., Yang, K.X., Han, X., Yao, Y.Q., Li, J., Wu, H.Y., Wan, S., Liu, L., Liu, D.Q., Kuang, Y.W., He, Z.P., Shang, P., Guo, C., Zheng, R.H., Tian, K., Zhu, Z.C., Liu, N.L., Lu, C.Y., Shu, R., Chen, Y.A., Peng, C.Z., Wang, J.Y., Pan, J.W.: Ground-to-satellite quantum teleportation. Nature 549(7670), 70–73 (2017)

doi: 10.1038/nature23675

Zhong, H.,Wang, H., Deng, Y., Chen, M., Peng, L., Luo, Y., Qin, J., Wu, D., Ding, X., Hu, Y., Hu, P., Yang, X., Zhang, W., Li, H., Li, Y., Jiang, X., Gan, L., Yang, G., You, L., Wang, Z., Li, L., Liu, N., Lu, C., Pan, J.: Quantum computational advantage using photons. arXiv:2012.01625v1 [quant-ph] (2020)

Zhong, H.S., Deng, Y.H., Qin, J., Wang, H., Chen, M.C., Peng, L.C., Luo, Y.H., Wu, D., Gong, S.Q., Su, H., Hu, Y., Hu, P., Yang, X.Y., Zhang, W.J., Li, H., Li, Y., Jiang, X., Gan, L., Yang, G., You, L., Wang, Z., Li, L., Liu, N.L., Renema, J.J., Lu, C.Y., Pan, J.W.: Phase-programmable Gaussian boson sampling using stimulated squeezed light. Phys. Rev. Lett. 127, 180502 (2021)

doi: 10.1103/PhysRevLett.127.180502

Madsen, L.S., Laudenbach, F., Askarani, M.F., Rortais, F., Vincent, T., Bulmer, J.F.F., Miatto, F.M., Neuhaus, L., Helt, L.G., Collins, M.J., Lita, A.E., Gerrits, T., Nam, S.W., Vaidya, V.D., Menotti, M., Dhand, I., Vernon, Z., Quesada, N., Lavoie, J.: Quantum computational advantage with a programmable photonic processor. Nature 606(7912), 75–81 (2022)

doi: 10.1038/s41586-022-04725-x

Carolan, J., Harrold, C., Sparrow, C., Martín-López, E., Russell, N.J., Silverstone, J.W., Shadbolt, P.J., Matsuda, N., Oguma, M., Itoh, M., Marshall, G.D., Thompson, M.G., Matthews, J.C.F., Hashimoto, T., O’Brien, J.L., Laing, A.: Universal linear optics. Science 349, 711 (2015)

doi: 10.1126/science.aab3642

Qiang, X., Zhou, X., Wang, J., Wilkes, C.M., Loke, T., O’Gara, S., Kling, L., Marshall, G.D., Santagati, R., Ralph, T.C., Wang, J.B., O’Brien, J.L., Thompson, M.G., Matthews, J.C.F.: Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photonics 12, 534–539 (2018)

doi: 10.1038/s41566-018-0236-y

Santagati, R., Silverstone, J.W., Strain, M.J., Sorel, M., Miki, S., Yamashita, T., Fujiwara, M., Sasaki, M., Terai, H., Tanner, M.G., Natarajan, C.M., Hadfield, R.H., O’Brien, J.L., Thompson, M.G.: Silicon photonic processor of two-qubit entangling quantum logic. J. Opt. 19, 114006 (2017)

doi: 10.1088/2040-8986/aa8d56

Taballione, C., Wolterink, T.A.W., Lugani, J., Eckstein, A., Bell, B.A., Grootjans, R., Visscher, I., Geskus, D., Roeloffzen, C.G.H., Renema, J.J., Walmsley, I.A., Pinkse, P.W.H., Boller, K.J.: [Formula: see text] reconfigurable quantum photonic processor based on silicon nitride waveguides. Opt. Express 27, 26842–26857 (2019)

doi: 10.1364/OE.27.026842

Ribeiro, A., Ruocco, A., Vanacker, L., Bogaerts, W.: Demonstration of a [Formula: see text]-port universal linear circuit. Optica 3, 1348–1357 (2016)

doi: 10.1364/OPTICA.3.001348

Koteva, K.I., Gentile, A.A., Flynn, B., Paesani, S., Laing, A.: Silicon quantum photonic device for multidimensional controlled unitaries. In: Frontiers in Optics/ Laser Science. FTu8D.1. Optical Society of America (2020)

Harris, N.C., Steinbrecher, G.R., Prabhu, M., Lahini, Y., Mower, J., Bunandar, D., Chen, C., Wong, F.N.C., Baehr-Jones, T., Hochberg, M., Lloyd, S., Englund, D.: Quantum transport simulations in a programmable nanophotonic processor. Nat. Photonics 11, 447–452 (2017)

doi: 10.1038/nphoton.2017.95

Sparrow, C., Martin-Lopez, E., Maraviglia, N., Neville, A., Harrold, C., Carolan, J., Joglekar, Y.N., Hashimoto, T., Matsuda, N., O’Brien, J.L., Tew, D.P., Laing, A.: Simulating the vibrational quantum dynamics of molecules using photonics. Nature 557(7707), 660 (2018)

doi: 10.1038/s41586-018-0152-9

Carolan, J., Mohseni, M., Olson, J.P., Prabhu, M., Chen, C., Bunandar, D., Niu, M.Y., Harris, N.C., Wong, F.N.C., Hochberg, M., Lloyd, S., Englund, D.: Variational quantum unsampling on a quantum photonic processor. Nat. Phys. 16, 322–327 (2020)

doi: 10.1038/s41567-019-0747-6

Spring, J.B., Metcalf, B.J., Humphreys, P.C., Kolthammer, W.S., Jin, X., Barbieri, M., Datta, A., Thomaspeter, N., Langford, N.K., Kundys, D., Gates, J.C., Smith, B.J., Smith, P.G.R., Walmsley, I.A.: Boson sampling on a photonic chip. Science 339(6121), 798 (2013)

doi: 10.1126/science.1231692

Tillmann, M., Dakić, B., Heilmann, R., Nolte, S., Szameit, A., Walther, P.: Experimental boson sampling. Nat. Photonics 7, 540–544 (2013)

doi: 10.1038/nphoton.2013.102

Shadbolt, P.J., Verde, M.R., Peruzzo, A., Politi, A., Laing, A., Lobino, M., Matthews, J.C.F., Thompson, M.G., O’Brien, J.L.: Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nat. Photonics 6, 45–49 (2012)

doi: 10.1038/nphoton.2011.283

Paesani, S., Ding, Y., Santagati, R., Chakhmakhchyan, L., Vigliar, C., Rottwitt, K., Oxenløwe, L.K., Wang, J., Thompson, M.G., Laing, A.: Generation and sampling of quantum states of light in a silicon chip. Nat. Phys. 15, 925–929 (2019)

doi: 10.1038/s41567-019-0567-8

Steinbrecher, G.R., Olson, J.P., Englund, D., Carolan, J.: Quantum optical neural networks. Npj Quantum Inf. 5, 60 (2019)

doi: 10.1038/s41534-019-0174-7

Shen, Y., Harris, N.C., Skirlo, S., Prabhu, M., Baehr-Jones, T., Hochberg, M., Sun, X., Zhao, S., Larochelle, H., Englund, D., Soljačić, M.: Deep learning with coherent nanophotonic circuits. Nat. Photonics 11, 441–446 (2017)

doi: 10.1038/nphoton.2017.93

Gentile, A. A., Flynn, B., Knauer, S., Wiebe, N., Paesani, S., Granade, C., Rarity, J., Santagati, R., Laing, A.: Learning models of quantum systems from experiments. arXiv:2002.06169 (2020)

Saggio, V., Asenbeck, B.E., Hamann, A., Strömberg, T., Schiansky, P., Dunjko, V., Friis, N., Harris, N.C., Hochberg, M., Englund, D., Wölk, S., Briegel, H.J., Walther, P.: Experimental quantum speed-up in reinforcement learning agents. Nature 591, 229–233 (2021)

doi: 10.1038/s41586-021-03242-7

Feldmann, J., Youngblood, N., Karpov, M., Gehring, H., Li, X., Stappers, M., Le Gallo, M., Fu, X., Lukashchuk, A., Raja, A.S., Liu, J., Wright, C.D., Sebastian, A., Kippenberg, T.J., Pernice, W.H.P., Bhaskaran, H.: Parallel convolutional processing using an integrated photonic tensor core. Nature 589, 52–58 (2021)

doi: 10.1038/s41586-020-03070-1

Zhuang, L., Roeloffzen, C.G., Hoekman, M., Boller, K.J., Lowery, A.J.: Programmable photonic signal processor chip for radiofrequency applications. Optica 2, 854–859 (2015)

doi: 10.1364/OPTICA.2.000854

Pérez, D., Gasulla, I., Crudgington, L., Thomson, D.J., Khokhar, A.Z., Li, K., Cao, W., Mashanovich, G.Z., Capmany, J.: Multipurpose silicon photonics signal processor core. Nat. Commun. 8, 1925 (2017)

doi: 10.1038/s41467-017-01529-w

Lee, Y., Bersin, E., Dahlberg, A., Wehner, S., Englund, D.: A quantum router architecture for high-fidelity entanglement flows in quantum networks, arXiv:2005.01852 (2020)

Chen, K. C., Bersin, E., Englund, D.: A polarization encoded photon-to-spin interface. arXiv:2004.02381 (2020)

Wan, N.H., Lu, T.J., Chen, K.C., Walsh, M.P., Trusheim, M.E., De Santis, L., Bersin, E.A., Harris, I.B., Mouradian, S.L., Christen, I.R., Bielejec, E.S., Englund, D.: Large-scale integration of artificial atoms in hybrid photonic circuits. Nature 583, 226–231 (2020)

doi: 10.1038/s41586-020-2441-3

Choi, H., Pant, M., Guha, S., Englund, D.: Percolation based architecture for cluster state creation using photonmediated entanglement between atomic memories. arXiv:1704.07292 (2019)

Reck, M., Zeilinger, A., Bernstein, H.J., Bertani, P.: Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58 (1994)

doi: 10.1103/PhysRevLett.73.58

Clements, W.R., Humphreys, P.C., Metcalf, B.J., Kolthammer, W.S., Walmsley, I.A.: Optimal design for universal multiport interferometers. Optica 3, 1460–1465 (2016)

doi: 10.1364/OPTICA.3.001460

Chuang, I.L., Yamamoto, Y.: Simple quantum computer. Phys. Rev. A 52(5), 3489 (1995)

doi: 10.1103/PhysRevA.52.3489

Wang, J., Sciarrino, F., Laing, A., Thompson, M.G.: Integrated photonic quantum technologies. Nat. Photon. 14, 273–284 (2020)

doi: 10.1038/s41566-019-0532-1

Piergentili, P., Amanti, F., Andrini, G., Armani, F., Bellani, V., Bonaiuto, V., Cammarata, S., Campostrini, M., Cornia, S., Dao, T.H., De Matteis, F., Demontis, V., Di Giuseppe, G., Ditalia Tchernij, S., Donati, S., Fontana, A., Forneris, J., Francini, R., Frontini, L., Gunnella, R., Iadanza, S., Kaplan, A.E., Lacava, C., Liberali, V., Marzioni, F., Nieto Hernández, E., Pedreschi, E., Prete, D., Prosposito, P., Rigato, V., Roncolato, C., Rossella, F., Salamon, A., Salvato, M., Sargeni, F., Shojaii, J., Spinella, F., Stabile, A., Toncelli, A., Trucco, G., Vitali, V.: Quantum information with integrated photonics. Appl. Sci. 14(1), 387 (2024)

Politi, A., Matthews, J.C.F., O’Brien, J.L.: Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221 (2009)

doi: 10.1126/science.1173731

Smith, B.J., Kundys, D., Thomas-Peter, N., Smith, P.G.R., Walmsley, I.A.: Phase-controlled integrated photonic quantum circuits. Opt. Express 17, 13516–13525 (2009)

doi: 10.1364/OE.17.013516

Peruzzo, A., Lobino, M., Matthews, J.C.F., Matsuda, N., Politi, A., Poulios, K., Zhou, X.Q., Lahini, Y., Ismail, N., Wörhoff, K., Bromberg, Y., Silberberg, Y., Thompson, M.G., OBrien, J.L.: Quantum walks of correlated photons. Science 329, 1500–1503 (2010)

doi: 10.1126/science.1193515

Laing, A., Peruzzo, A., Politi, A., Verde, M.R., Halder, M., Ralph, T.C., Thompson, M.G., O’Brien, J.L.: High-fidelity operation of quantum photonic circuits. Appl. Phys. Lett. 97, 211109 (2010)

doi: 10.1063/1.3497087

Gerrits, T., Thomas-Peter, N., Gates, J.C., Lita, A.E., Metcalf, B.J., Calkins, B., Tomlin, N.A., Fox, A.E., Linares, A.L., Spring, J.B., Langford, N.K., Mirin, R.P., Smith, P.G.R., Walmsley, I.A., Nam, S.W.: On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing. Phys. Rev. A 84, 060301(R) (2011)

doi: 10.1103/PhysRevA.84.060301

Pernice, W., Schuck, C., Minaeva, O., Li, M., Goltsman, G.N., Sergienko, A.V., Tang, H.X.: High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits. Nat. Commun. 3, 1325 (2012)

doi: 10.1038/ncomms2307

Bonneau, D., Engin, E., Ohira, K., Suzuki, N., Yoshida, H., Iizuka, N., Ezaki, M., Natarajan, C.M., Tanner, M.G., Hadfield, R.H., Dorenbos, S.N., Zwiller, V., O’Brien, J.L., Thompson, M.G.: Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits. New J. Phys. 14, 045003 (2012)

doi: 10.1088/1367-2630/14/4/045003

Crespi, A., Osellame, R., Ramponi, R., Brod, D.J., Galvao, E.F., Spagnolo, N., Vitelli, C., Maiorino, E., Mataloni, P., Sciarrino, F.: Integrated multimode interferometers with arbitrary designs for photonic boson sampling. Nat. Photon. 7(7), 545 (2013)

doi: 10.1038/nphoton.2013.112

Broome, M.A., Fedrizzi, A., Rahimikeshari, S., Dove, J., Aaronson, S., Ralph, T.C., White, A.: Photonic boson sampling in a tunable circuit. Science 339(6121), 794 (2013)

doi: 10.1126/science.1231440

Carolan, J., Meinecke, J.D.A., Shadbolt, P.J., Russell, N.J., Ismail, N., Wörhoff, K., Rudolph, T., Thompson, M.G., O’Brien, J.L., Matthews, J.C.F., Laing, A.: On the experimental verification of quantum complexity in linear optics. Nat. Photon. 8, 621–626 (2014)

doi: 10.1038/nphoton.2014.152

Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., Osellame, R.: Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012)

doi: 10.1103/PhysRevLett.108.010502

He, Y.M., He, Y., Wei, Y.J., Wu, D., Atatüre, M., Schneider, C., Höfling, S., Kamp, M., Lu, C.Y., Pan, J.W.: On-demand semiconductor single-photon source with near-unity indistinguishability. Nat. Nanotechnol. 8, 213–217 (2013)

doi: 10.1038/nnano.2012.262

Silverstone, J., Bonneau, D., Ohira, K., Suzuki, N., Yoshida, H., Iizuka, N., Ezaki, M., Natarajan, C.M., Tanner, M.G., Hadfield, R.H., Zwiller, V., Marshall, G.D., Rarity, J.G., O’Brien, J.L., Thompson, M.G.: On-chip quantum interference between silicon photon-pair sources. Nat. Photon. 8, 104–108 (2014)

doi: 10.1038/nphoton.2013.339

Arcari, M., Söllner, I., Javadi, A., Lindskov Hansen, S., Mahmoodian, S., Liu, J., Thyrrestrup, H., Lee, E.H., Song, J.D., Stobbe, S., Lodahl, P.: Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide. Phys. Rev. Lett. 113, 093603 (2014)

doi: 10.1103/PhysRevLett.113.093603

Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.H., Zhou, X.Q., Love, P.J., Aspuru-Guzik, A., O’Brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014)

doi: 10.1038/ncomms5213

Wang, J., Bonneau, D., Villa, M., Silverstone, J.W., Santagati, R., Miki, S., Yamashita, T., Fujiwara, M., Sasaki, M., Terai, H., Tanner, M.G., Natarajan, C.M., Hadfield, R.H., O’Brien, J.L., Thompson, M.G.: Chip-to-chip quantum photonic interconnect by path-polarization interconversion. Optica 3, 407–413 (2016)

doi: 10.1364/OPTICA.3.000407

Sibson, P., Erven, C., Godfrey, M., Miki, S., Yamashita, T., Fujiwara, M., Sasaki, M., Terai, H., Tanner, M.G., Natarajan, C.M., Hadfield, R.H., O’Brien, J.L., Thompson, M.G.: Chip-based quantum key distribution. Nat. Commun. 8, 13984 (2017)

doi: 10.1038/ncomms13984

Spring, J.B., Mennea, P.L., Metcalf, B.J., Humphreys, P.C., Gates, J.C., Rogers, H.L., Söller, C., Smith, B.J., Kolthammer, W.S., Smith, P.G.R., Walmsley, I.A.: Chip-based array of near-identical, pure, heralded single-photon sources. Optica 4, 90–96 (2017)

doi: 10.1364/OPTICA.4.000090

Bentivegna, M., Spagnolo, N., Vitelli, C., Flamini, F., Viggianiello, N., Latmiral, L., Mataloni, P., Brod, D.J., Galvao, E.F., Crespi, A., Ramponi, R., Osellame, R., Sciarrino, F.: Experimental scattershot boson sampling. Sci. Adv. 1(3), e1400255 (2015)

doi: 10.1126/sciadv.1400255

Ciampini, M., Orieux, A., Paesani, S., Sciarrino, F., Corrielli, G., Crespi, A., Ramponi, R., Osellame, R., Mataloni, P.: Path-polarization hyperentangled and cluster states of photons on a chip. Light Sci. Appl. 5, e16064 (2016)

doi: 10.1038/lsa.2016.64

Wang, H., He, Y., Li, Y.H., Su, Z.E., Li, B., Huang, H.L., Ding, X., Chen, M.C., Liu, C., Qin, J., Li, J.P., He, Y.M., Schneider, C., Kamp, M., Peng, C.Z., Höfling, S., Lu, C.Y., Pan, J.W.: High-efficiency multiphoton boson sampling. Nat. Photon. 11(6), 361 (2017)

doi: 10.1038/nphoton.2017.63

Wang, J., Paesani, S., Santagati, R., Knauer, S., Gentile, A.A., Wiebe, N., Petruzzella, M., O’Brien, J.L., Rarity, J.G., Laing, A., Thompson, M.G.: Experimental quantum Hamiltonian learning. Nat. Phys. 13, 551–555 (2017)

doi: 10.1038/nphys4074

Wang, J.W., Paesani, S., Ding, Y., Santagati, R., Skrzypczyk, P., Salavrakos, A., Tura, J., Augusiak, R., Mančinska, L., Bacco, D., Bonneau, D., Silverstone, J.W., Gong, Q., Acín, A., Rottwitt, K., Oxenløwe, L.K., O’Brien, J.L., Laing, A., Thompson, M.G.: Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285–291 (2018)

Adcock, J.C., Vigliar, C., Santagati, R., Silverstone, J.W., Thompson, M.G.: Programmable four-photon graph states on a silicon chip. Nat. Commun. 10, 3528 (2019)

doi: 10.1038/s41467-019-11489-y

Wang, H., Qin, J., Ding, X., Chen, M.C., Chen, S., You, X., He, Y.M., Jiang, X., You, L., Wang, Z., Schneider, C., Renema, J.J., Höfling, S., Lu, C.Y., Pan, J.W.: Boson sampling with 20 input photons and a 60-mode interferometer in a 1014-dimensional Hilbert space. Phys. Rev. Lett. 123, 250503 (2019)

doi: 10.1103/PhysRevLett.123.250503

Arrazola, J.M., Bergholm, V., Brádler, K., Bromley, T.R., Collins, M.J., Dhand, I., Fumagalli, A., Gerrits, T., Goussev, A., Helt, L.G., Hundal, J., Isacsson, T., Israel, R.B., Izaac, J., Jahangiri, S., Janik, R., Killoran, N., Kumar, S.P., Lavoie, J., Lita, A.E., Mahler, D.H., Menotti, M., Morrison, B., Nam, S.W., Neuhaus, L., Qi, H.Y., Quesada, N., Repingon, A., Sabapathy, K.K., Schuld, M., Su, D., Swinarton, J., Száva, A., Tan, K., Tan, P., Vaidya, V.D., Vernon, Z., Zabaneh, Z., Zhang, Y.: Quantum circuits with many photons on a programmable nanophotonic chip. Nature 591, 54–60 (2021)

doi: 10.1038/s41586-021-03202-1

Zhang, M., Feng, L., Li, M., Chen, Y., Zhang, L., He, D., Guo, G., Guo, G., Ren, X., Dai, D.: Supercompact photonic quantum logic gate on a silicon chip. Phys. Rev. Lett. 126, 130501 (2021)

doi: 10.1103/PhysRevLett.126.130501

Gyger, S., Zichi, J., Schweickert, L., Elshaari, A.W., Steinhauer, S., Covre Da Silva, S.F., Rastelli, A., Zwiller, V., Jöns, K.D., Errando-Herranz, C.: Reconfigurable photonics with on-chip single-photon detectors. Nat. Commun. 12, 1408 (2021)

doi: 10.1038/s41467-021-21624-3

Chen, Y.A., Zhang, Q., Chen, T.Y., Cai, W.Q., Liao, S.K., Zhang, J., Chen, K., Yin, J., Ren, J.G., Chen, Z., Han, S.L., Yu, Q., Liang, K., Zhou, F., Yuan, X., Zhao, M.S., Wang, T.Y., Jiang, X., Zhang, L., Liu, W.Y., Li, Y., Shen, Q., Cao, Y., Lu, C.Y., Shu, R., Wang, J.Y., Li, L., Liu, N.L., Xu, F., Wang, X.B., Peng, C.Z., Pan, J.W.: An integrated space-to-ground quantum communication network over 4,600 kilometers. Nature 589, 214–219 (2021)

Chi, Y., Huang, J., Zhang, Z., Mao, J., Zhou, Z., Chen, X., Zhai, C., Bao, J., Dai, T., Yuan, H., Zhang, M., Dai, D., Tang, B., Yang, Y., Li, Z., Ding, Y., Oxenløwe, L.K., Thompson, M.G., O’Brien, J.L., Li, Y., Gong, Q., Wang, J.: A programmable Qudit-based quantum processor. Nat. Commun. 13, 1166 (2022)

doi: 10.1038/s41467-022-28767-x

Zheng, Y., Zhai, C., Liu, D., Mao, J., Chen, X., Dai, T., Huang, J., Bao, J., Fu, Z., Tong, Y., Zhou, X., Yang, Y., Tang, B., Li, Z., Li, Y., Gong, Q., Tsang, H.K., Dai, D., Wang, J.: Multichip multidimensional quantum networks with entanglement retrievability. Science 381, 221–226 (2023)

doi: 10.1126/science.adg9210

Ono, T., Roga, W., Wakui, K., Fujiwara, M., Miki, S., Terai, H., Takeoka, M.: Demonstration of a Bosonic quantum classifier with data reuploading. Phys. Rev. Lett. 131, 013601 (2023)

doi: 10.1103/PhysRevLett.131.013601

Bao, J., Fu, Z., Pramanik, T., Mao, J., Chi, Y., Cao, Y., Zhai, C., Mao, Y., Dai, T., Chen, X., Jia, X., Zhao, L., Zheng, Y., Tang, B., Li, Z., Luo, J., Wang, W., Yang, Y., Peng, Y., Liu, D., Dai, D., He, Q., Muthali, A.L., Oxenløwe, L.K., Vigliar, C., Paesani, S., Hou, H., Santagati, R., Silverstone, J.W., Laing, A., Thompson, M.G., O’Brien, J.L., Ding, Y., Gong, Q., Wang, J.: Very-large-scale integrated quantum graph photonics. Nat. Photon. 17, 573–581 (2023)

Deng, Y.H., Gu, Y.C., Liu, H.L., Gong, S.Q., Su, H., Zhang, Z.J., Tang, H.Y., Jia, M.H., Xu, J.M., Chen, M.C., Qin, J., Peng, L.C., Yan, J., Hu, Y., Huang, J., Li, H., Li, Y., Chen, Y., Jiang, X., Gan, L., Yang, G., You, L., Li, L., Zhong, H.S., Wang, H., Liu, N.L., Renema, J.J., Lu, C.Y., Pan, J.W.: Gaussian boson sampling with pseudo-photon-number-resolving detectors and quantum computational advantage. Phys. Rev. Lett. 131(15), 131 (2023)

The Nobel Prize in Physics 2022. NobelPrize.org. Nobel Prize Outreach AB 2023. Available at the website of nobelprize.org/prizes/physics/2022/summary/ (2023)

Clauser, J.F., Shimony, A.: Bell’s theorem: experimental tests and implications. Rep. Prog. Phys. 41, 1881–1927 (1978)

doi: 10.1088/0034-4885/41/12/002

Barreiro, J.T., Langford, N.K., Peters, N.A., Kwiat, P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)

doi: 10.1103/PhysRevLett.95.260501

Fedrizzi, A., Herbst, T., Poppe, A., Jennewein, T., Zeilinger, A.: A wavelength-tunable fiber-coupled source of narrowband entangled photons. Opt. Express 15, 15377–15386 (2007)

doi: 10.1364/OE.15.015377

Cohen, O., Lundeen, J.S., Smith, B.J., Puentes, G., Mosley, P.J., Walmsley, I.A.: Tailored photon-pair generation in optical fibers. Phys. Rev. Lett. 102, 123603 (2009)

doi: 10.1103/PhysRevLett.102.123603

Langford, N., Ramelow, S., Prevedel, R., Munro, W.J., Milburn, G.J., Zeilinger, A.: Efficient quantum computing using coherent photon conversion. Nature 478, 360–363 (2011)

doi: 10.1038/nature10463

AbuGhanem, M., Eleuch, H.: Two-qubit entangling gates for superconducting quantum computers. Results Phys. 56, 107236 (2024)

doi: 10.1016/j.rinp.2023.107236

AbuGhanem, M.: Comprehensive characterization of three-qubit Grover search algorithm on IBM's 127-qubit superconducting quantum computers. arXiv: 2406.16018 (2024)

AbuGhanem, M., Homid, A., Abdel-Aty, M.: Cavity control as a new quantum algorithms implementation treatment. Front. Phys. 13(1), 130303 (2018)

Politi, A., Cryan, M.J., Rarity, J.G., Yu, S., O’Brien, J.L.: Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008)

doi: 10.1126/science.1155441

Bromley, T.R., Arrazola, J.M., Jahangiri, S., Izaac, J., Quesada, N., Gran, A.D., Schuld, M., Swinarton, J., Zabaneh, Z., Killoran, N.: Applications of near-term photonic quantum computers: software and algorithms. Quantum Sci. Technol. 5, 034010 (2020)

doi: 10.1088/2058-9565/ab8504

Kues, M., Reimer, C., Roztocki, P., Cortés, L.R., Sciara, S., Wetzel, B., Zhang, Y., Cino, A., Chu, S.T., Little, B.E., Moss, D.J., Caspani, L., Azaña, J., Morandotti, R.: On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546, 622–626 (2017)

doi: 10.1038/nature22986

Kobayashi, T., Ikuta, R., Yasui, S., Miki, S., Yamashita, T., Terai, H., Yamamoto, T., Koashi, M., Imoto, N.: Frequency-domain Hong-Ou-Mandel interference. Nat. Photon. 10, 441–444 (2016)

doi: 10.1038/nphoton.2016.74

Lukens, J.M., Lougovski, P.: Frequency-encoded photonic qubits for scalable quantum information processing. Optica 4, 8–16 (2017)

doi: 10.1364/OPTICA.4.000008

Lu, H.H., Lukens, J.M., Peters, N.A., Odele, O.D., Leaird, D.E., Weiner, A.M., Lougovski, P.: Electro-optic frequency beam splitters and tritters for high-fidelity photonic quantum information processing. Phys. Rev. Lett. 120, 30502 (2018)

doi: 10.1103/PhysRevLett.120.030502

Joshi, C., Farsi, A., Dutt, A., Kim, B.Y., Ji, X., Zhao, Y., Bishop, A.M., Lipson, M., Gaeta, A.L.: Frequency-domain quantum interference with correlated photons from an integrated microresonator. Phys. Rev. Lett. 124, 143601 (2020)

doi: 10.1103/PhysRevLett.124.143601

Kues, M., Reimer, C., Lukens, J.M., Munro, W.J., Weiner, A.M., Moss, D.J., Morandotti, R.: Quantum optical microcombs. Nat. Photon. 13, 170–179 (2019)

doi: 10.1038/s41566-019-0363-0

Hu, Y., Yu, M., Zhu, D., Sinclair, N., Shams-Ansari, A., Shao, L., Holzgrafe, J., Puma, E., Zhang, M., Lončar, M.: On-chip electro-optic frequency shifters and beam splitters. Nature 599, 587–593 (2021)

doi: 10.1038/s41586-021-03999-x

Miller, D.A.B.: Perfect optics with imperfect components. Optica 2, 747–750 (2015)

doi: 10.1364/OPTICA.2.000747

Taballione, C., van der Meer, R., Snijders, H.J., Hooijschuur, P., Epping, J.P., de Goede, M., Kassenberg, B., Venderbosch, P., Toebes, C., van den Vlekkert, H., Pinkse, P.W.H., Renema, J.J.: A universal fully reconfigurable 12-mode quantum photonic processor. Mater. Quantum Technol. 1, 035002 (2021)

doi: 10.1088/2633-4356/ac168c

Cerf, N.J., Adami, C., Kwiat, P.G.: Optical simulation of quantum logic. Phys. Rev. A 57(3), 1477 (1998)

doi: 10.1103/PhysRevA.57.R1477

Milburn, G.J.: Quantum optical fredkin gate. Phys. Rev. Lett. 62(18), 2124 (1989)

doi: 10.1103/PhysRevLett.62.2124

Kok, P., Lee, H., Dowling, J.P.: Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements. Phys. Rev. A 66(6), 063814 (2002)

doi: 10.1103/PhysRevA.66.063814

Ralph, T.C., Langford, N.K., Bell, T.B., White, A.G.: Linear optical controlled-NOT gate in the coincidence basis. Phys. Rev. A 65, 062324 (2001)

doi: 10.1103/PhysRevA.65.062324

Weedbrook, C., Pirandola, S., García-Patrón, R., Cerf, N.J., Ralph, T.C., Shapiro, J.H., Lloyd, S.: Gaussian quantum information. Rev. Mod. Phys. 84(2), 621 (2012)

doi: 10.1103/RevModPhys.84.621

Braunstein, S.L., Van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77(2), 513 (2005)

doi: 10.1103/RevModPhys.77.513

Adesso, G., Ragy, S., Lee, A.R.: Continuous variable quantum information: Gaussian states and beyond. Open. Syst. Inf. Dyn. 21(01n02), 1440001 (2014)

doi: 10.1142/S1230161214400010

Serafini, A.: Quantum continuous variables: a primer of theoretical methods. Routledge, New York (2017)

doi: 10.1201/9781315118727

Balthazar, W.F., Caetano, D.P., Souza, C.E.R., Huguenin, J.A.O.: Using polarization to control the phase of spatial modes for application in quantum information. Braz. J. Phys. 44(6), 658 (2014)

doi: 10.1007/s13538-014-0250-6

Milione, G., Nguyen, T.A., Leach, J., Nolan, D.A., Alfano, R.R.: Using the nonseparability of vector beams to encode information for optical communication. Opt. Lett. 40(21), 4887 (2015)

doi: 10.1364/OL.40.004887

Souza, C.E.R., Borges, C.V.S., Khoury, A.Z., Huguenin, J.A.O., Aolita, L., Walborn, S.P.: Quantum key distribution without a shared reference frame. Phys. Rev. A 77, 032345 (2008)

doi: 10.1103/PhysRevA.77.032345

Obando, P.C., Passos, M.H.M., Paula, F.M., Huguenin, J.A.O.: Simulating Markovian quantum decoherence processes through an all-optical setup. Quant. Inf. Process. 19(7), 1573 (2020)

Khoury, A.Z., Milman, P.: Quantum teleportation in the spin-orbit variables of photon pairs. Phys. Rev. A 83, 060301 (2011)

doi: 10.1103/PhysRevA.83.060301

Passos, M.H.M., Obando, P.C., Balthazar, W.F., Paula, F.M., Huguenin, J.A.O., Sarandy, M.S.: Non-Markovianity through quantum coherence in an all-optical setup. Opt. Lett. 44(10), 2478 (2019)

doi: 10.1364/OL.44.002478

Passos, M.H.M., Santos, A.C., Sarandy, M.S., Huguenin, J.A.O.: Optical simulation of a quantum thermal machine. Phys. Rev. A 100, 022113 (2019)

doi: 10.1103/PhysRevA.100.022113

Passos, M.H.M., Balthazar, W.F., Khoury, A.Z., Hor-Meyll, M., Davidovich, L., Huguenin, J.A.O.: Experimental investigation of environment-induced entanglement using an all-optical setup. Phys. Rev. A 97, 022321 (2018)

doi: 10.1103/PhysRevA.97.022321

Pallister, S., Linden, N., Montanaro, A.: Optimal verification of entangled states with local measurements. Phys. Rev. Lett. 120, 170502 (2018)

doi: 10.1103/PhysRevLett.120.170502

Zhu, H., Hayashi, M.: Efficient verification of pure quantum states in the adversarial scenario. Phys. Rev. Lett. 123, 260504 (2019)

doi: 10.1103/PhysRevLett.123.260504

Li, Z., Han, Y.H., Zhu, H.: Efficient verification of bipartite pure states. Phys. Rev. A 100, 032316 (2019)

doi: 10.1103/PhysRevA.100.032316

Wang, K., Hayashi, M.: Optimal verification of two-qubit pure states. Phys. Rev. A 100, 032315 (2019)

doi: 10.1103/PhysRevA.100.032315

Sugiyama, T., Turner, P.S., Murao, M.: Precision-guaranteed quantum tomography. Phys. Rev. Lett. 111, 160406 (2013)

doi: 10.1103/PhysRevLett.111.160406

Gonzales, J.P., Sánchez, P., Auccapuclla, F., Miller, B., Andrés, M.V., De Zela, F.: Unrestricted generation of pure two-qubit states and entanglement diagnosis by single-qubit tomography. Opt. Lett. 44(13), 3310–3313 (2019)

doi: 10.1364/OL.44.003310

Starek, R., Miková, M., Straka, I., Dušek, M., Ježek, M., Fiurášek, J., Mičuda, M.: Experimental realization of SWAP operation on hyper-encoded qubits. Opt. Express 26(7), 8443–8452 (2018)

doi: 10.1364/OE.26.008443

Ruelas, D.R.A., Paredes, C.M., Marrou, J.P., Yugra, Y., Uria, M., Massoni, E., De Zela, F.: Synthesis and characterization of pure, two-qubit states encoded in path and polarization. J. Opt. 23, 085201 (2021)

doi: 10.1088/2040-8986/ac1bbf

Kwek, L.C., Cao, L., Luo, W., Wang, Y., Sun, S., Wang, X., Liu, A.Q.: Chip-based quantum key distribution. AAPPS Bull. 31(1), 1–8 (2021)

doi: 10.1007/s43673-021-00017-0

Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81(3), 1301 (2009)

doi: 10.1103/RevModPhys.81.1301

Xu, F., Ma, X., Zhang, Q., Lo, H.K., Pan, J.W.: Secure quantum key distribution with realistic devices. Rev. Mod. Phys. 92(2), 025002 (2020)

doi: 10.1103/RevModPhys.92.025002

Myers, C., Laflamme, R.: Linear optics quantum computation: an overview. arXiv preprint quant-ph/0512104 (2005)

Bourassa, J.E., Alexander, R.N., Vasmer, M., Patil, A., Tzitrin, I., Matsuura, T., Su, D., Baragiola, B.Q., Guha, S., Dauphinais, G., Sabapathy, K.K., Menicucci, N.C., Dhand, I.: Blueprint for a scalable photonic fault-tolerant quantum computer. Quantum 5, 392 (2021)

doi: 10.22331/q-2021-02-04-392

Barzanjeh, S., Xuereb, A., Gröblacher, S., Paternostro, M., Regal, C.A., Weig, E.M.: Optomechanics for quantum technologies. Nat. Phys. 18, 15–24 (2022)

doi: 10.1038/s41567-021-01402-0

Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86(4), 1391 (2014)

doi: 10.1103/RevModPhys.86.1391

Wang, S., Yin, Z.Q., He, D.Y., Chen, W., Wang, R.Q., Ye, P., Zhou, Y., Fan-Yuan, G.J., Wang, F.X., Chen, W., Zhu, Y.G., Morozov, P.V., Divochiy, A.V., Zhou, Z., Guo, G.C., Han, Z.F.: Twin-field quantum key distribution over 830-km fibre. Nat. Photon. 16, 154–161 (2022)

doi: 10.1038/s41566-021-00928-2

Li, W., Zhang, L., Tan, H., Lu, Y., Liao, S.K., Huang, J., Li, H., Wang, Z., Mao, H.K., Yan, B., Li, Q., Liu, Y., Zhang, Q., Peng, C.Z., You, L., Xu, F., Pan, J.W.: High-rate quantum key distribution exceeding 110 Mb [Formula: see text]. Nat. Photon. 17, 416–421 (2023)

Clementi, M., Sabattoli, F.A., Borghi, M., Gianini, L., Tagliavacche, N., El Dirani, H., Youssef, L., Bergamasco, N., Petit-Etienne, C., Pargon, E., Sipe, J.E., Liscidini, M., Sciancalepore, C., Galli, M., Bajoni, D.: Programmable frequency-bin quantum states in a nano-engineered silicon device. Nat. Commun. 14, 176 (2023)

doi: 10.1038/s41467-022-35773-6

Brendel, J., Gisin, N., Tittel, W., Zbinden, H.: Pulsed energy-time entangled twin-photon source for quantum communication. Phys. Rev. Lett. 82, 2594 (1999)

doi: 10.1103/PhysRevLett.82.2594

Marcikic, I., de Riedmatten, H., Tittel, W., Scarani, V., Zbinden, H., Gisin, N.: Time-bin entangled qubits for quantum communication created by femtosecond pulses. Phys. Rev. A 66, 062308 (2002)

doi: 10.1103/PhysRevA.66.062308

Marcikic, I., de Riedmatten, H., Tittel, W., Zbinden, H., Legré, M., Gisin, N.: Distribution of time-bin entangled qubits over 50 km of optical fiber. Phys. Rev. Lett. 93, 180502 (2004)

doi: 10.1103/PhysRevLett.93.180502

Inagaki, T., Matsuda, N., Tadanaga, O., Asobe, M., Takesue, H.: Entanglement distribution over 300 km of fiber. Opt. Express 21, 23241–23249 (2013)

doi: 10.1364/OE.21.023241

Silverstone, J.W., Santagati, R., Bonneau, D., Strain, M.J., Sorel, M., O’Brien, J.L., Thompson, M.G.: Qubit entanglement between ring-resonator photon-pair sources on a silicon chip. Nat. Commun. 6, 7948 (2015)

doi: 10.1038/ncomms8948

Kwiat, P.G., Waks, E., White, A.G., Appelbaum, I., Eberhard, P.H.: Ultrabright source of polarization-entangled photons. Phys. Rev. A 60, R773–R776 (1999)

doi: 10.1103/PhysRevA.60.R773

Sansoni, L., Sciarrino, F., Vallone, G., Mataloni, P., Crespi, A., Ramponi, R., Osellame, R.: Polarization entangled state measurement on a chip. Phys. Rev. Lett. 105, 200503 (2010)

doi: 10.1103/PhysRevLett.105.200503

Ursin, R., Tiefenbacher, F., Schmitt-Manderbach, T., Weier, H., Scheidl, T., Lindenthal, M., Blauensteiner, B., Jennewein, T., Perdigues, J., Trojek, P., Ömer, B., Fürst, M., Meyenburg, M., Rarity, J., Sodnik, Z., Barbieri, C., Weinfurter, H., Zeilinger, A.: Entanglement-based quantum communication over 144 km. Nat. Phys. 3, 481–486 (2007)

doi: 10.1038/nphys629

Zeuner, J., Sharma, A.N., Tillmann, M., Heilmann, R., Gräfe, M., Moqanaki, A., Szameit, A., Walther, P.: Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits. npj Quantum Inf. (2018)

Crespi, A., Ramponi, R., Osellame, R., Sansoni, L., Bongioanni, I., Sciarrino, F., Vallone, G., Mataloni, P.: Integrated photonic quantum gates for polarization qubits. Nat. Commun. 2, 566 (2011)

doi: 10.1038/ncomms1570

Marshall, G.D., Politi, A., Matthews, J.C.F., Dekker, P., Ams, M., Withford, M.J., O’Brien, J.L.: Laser written waveguide photonic quantum circuits. Opt. Express 17, 12546–12554 (2009)

doi: 10.1364/OE.17.012546

Davis, K.M., Miura, K., Sugimoto, N., Hirao, K.: Writing waveguides in glass with a femtosecond laser. Opt. Lett. 21, 1729–1731 (1996)

doi: 10.1364/OL.21.001729

Zewail, A.H.: Femtochemistry. Laser Sci. 242, 4886 (1988)

Zewail, A.H.: Femtochemistry: recent progress in studies of dynamics and control of reactions and their transition states. J. Phys. Chem. 100, 31 (1996)

doi: 10.1021/jp960658s

Zewail, A.H.: Femtochemistry: atomic-scale dynamics of the chemical bond using ultrafast lasers (Nobel Lecture). Angewandte Chemie International Edition, 2000—Wiley Online Library (2000)

Kok, P., Lovett, B.W.: Introduction to Optical Quantum Information Processing. Cambridge University Press (2010)

doi: 10.1017/CBO9781139193658

Hou, Z., Xiang, G., Dong, D., Li, C.F., Guo, G.C.: Realization of mutually unbiased bases for a qubit with only one wave plate: theory and experiment. Opt. Express 23, 10018–10031 (2015)

doi: 10.1364/OE.23.010018

Prevedel, R., Walther, P., Tiefenbacher, F., Böhi, P., Kaltenbaek, R., Jennewein, T., Zeilinger, A.: High-speed linear optics quantum computing using active feed-forward. Nature 445, 65–69 (2007)

doi: 10.1038/nature05346

Heilmann, R., Gräfe, M., Nolte, S., Szameit, A.: Arbitrary photonic wave plate operations on chip: realizing Hadamard, Pauli-X and rotation gates for polarisation qubits. Sci. Rep. 4, 4118 (2014)

doi: 10.1038/srep04118

Barz, S., Kassal, I., Ringbauer, M., Lipp, Y.O., Dakić, B., Aspuru-Guzik, A., Walther, P.: A two-qubit photonic quantum processor and its application to solving systems of linear equations. Sci. Rep. 4, 6115 (2014)

doi: 10.1038/srep06115

Matthews, J., Poulios, K., Meinecke, J., Politi, A., Peruzzo, A., Ismail, N., Wörhoff, K., Thompson, M.G., O’Brien, J.L.: Observing fermionic statistics with photons in arbitrary processes. Sci. Rep. 3, 1539 (2013)

doi: 10.1038/srep01539

Ma, C., Sacher, W.D., Tang, Z., Mikkelsen, J.C., Yang, Y., Feihu, X., Thiessen, T., Lo, H.K., Poon, J.K.S.: Silicon photonic transmitter for polarization-encoded quantum key distribution. Optica 3, 1274–1278 (2016)

doi: 10.1364/OPTICA.3.001274

Kim, Y.-H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete bell state measurement. Phys. Rev. Lett. 86, 1370 (2001)

doi: 10.1103/PhysRevLett.86.1370

Vallés, A., Hendrych, M., Svozilík, J., Machulka, R., Abolghasem, P., Kang, D., Bijlani, B.J., Helmy, A.S., Torres, J.P.: Generation of polarization-entangled photon pairs in a Bragg reflection waveguide. Opt. Express 21, 10841–10849 (2013)

doi: 10.1364/OE.21.010841

Olislager, L., Safioui, J., Clemmen, S., Huy, K.P., Bogaerts, W., Baets, R., Emplit, P., Massar, S.: Silicon-on-insulator integrated source of polarization-entangled photons. Opt. Lett. 38, 1960–1962 (2013)

doi: 10.1364/OL.38.001960

Matsuda, N., Le Jeannic, H., Fukuda, H., Tsuchizawa, T., Munro, W.J., Shimizu, K., Yamada, K., Tokura, Y., Takesue, H.: A monolithically integrated polarization entangled photon pair source on a silicon chip. Sci. Rep. 2, 817 (2012)

doi: 10.1038/srep00817

Kaiser, F., Ngah, L.A., Issautier, A., Delord, T., Aktas, D., D'Auria, V., De Micheli, M.P., Kastberg, A., Labonté, L., Alibart, O., Martin, A., Tanzilli, S.: Polarization entangled photon-pair source based on quantum nonlinear photonics and interferometry. Opt. Commun. 327, 7–16 (2014)

doi: 10.1016/j.optcom.2014.03.056

Hamel, D., Shalm, L., Hübel, H., Miller, A.J., Marsili, F., Verma, V.B., Mirin, R.P., Nam, S.W., Resch, K.J., Jennewein, T.: Direct generation of three-photon polarization entanglement. Nat. Photon. 8, 801–807 (2014)

doi: 10.1038/nphoton.2014.218

Barreiro, J.T., Wei, T.-C., Kwiat, P.G.: Remote preparation of single-photon “hybrid” entangled and vector-polarization states. Phys. Rev. Lett. 105, 030407 (2010)

doi: 10.1103/PhysRevLett.105.030407

Crespi, A., Longhi, S., Osellame, R.: Photonic realization of the quantum rabi model. Phys. Rev. Lett. 108, 163601 (2012)

doi: 10.1103/PhysRevLett.108.163601

Rojas-Rojas, S., Morales-Inostroza, L., Naether, U., Xavier, G.B., Nolte, S., Szameit, A., Vicencio, R.A., Lima, G., Delgado, A.: Analytical model for polarization-dependent light propagation in waveguide arrays and applications. Phys. Rev. A 90, 063823 (2014)

doi: 10.1103/PhysRevA.90.063823

Bonneau, D., Lobino, M., Jiang, P., Natarajan, C.M., Tanner, M.G., Hadfield, R.H., Dorenbos, S.N., Zwiller, V., Thompson, M.G., O’Brien, J.L.: Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices. Phys. Rev. Lett. 108, 053601 (2012)

doi: 10.1103/PhysRevLett.108.053601

Müller, M., Bounouar, S., Jöns, K., Glässl, M., Michler, P.: On-demand generation of indistinguishable polarization-entangled photon pairs. Nat. Photon. 8, 224–228 (2014)

doi: 10.1038/nphoton.2013.377

Bhatti, D., von Zanthier, J., Agarwal, G.S.: Entanglement of polarization and orbital angular momentum. Phys. Rev. A 91, 062303 (2015)

doi: 10.1103/PhysRevA.91.062303

Vallone, G., Ceccarelli, R., De Martini, F., Mataloni, P.: Hyperentanglement of two photons in three degrees of freedom. Phys. Rev. A 79, 030301(R) (2009)

doi: 10.1103/PhysRevA.79.030301

Orieux, A., Ciampini, M.A., Mataloni, P., Bruß, D., Rossi, M., Macchiavello, C.: Experimental generation of robust entanglement from classical correlations via local dissipation. Phys. Rev. Lett. 115, 160503 (2015)

doi: 10.1103/PhysRevLett.115.160503

Fickler, R., Lapkiewicz, R., Plick, W.N., Krenn, M., Schaeff, C., Ramelow, S., Zeilinger, A.: Quantum entanglement of high angular momenta. Science 338, 640–643 (2012)

doi: 10.1126/science.1227193

Nagali, E., Sciarrino, F., De Martini, F., Marrucci, L., Piccirillo, B., Karimi, E., Santamato, E.: Quantum information transfer from spin to orbital angular momentum of photons. Phys. Rev. Lett. 103, 013601 (2009)

doi: 10.1103/PhysRevLett.103.013601

Chen, T.Y., Zhang, J., Boileau, J.C., Jin, X.M., Yang, B., Zhang, Q., Yang, F.T., Laflamme, R., Pan, J.W.: Experimental quantum communication without a shared reference frame. Phys. Rev. Lett. 96, 150504 (2006)

doi: 10.1103/PhysRevLett.96.150504

Steinlechner, F., Ecker, S., Fink, M., Liu, B., Bavaresco, J., Huber, M., Scheidl, T., Ursin, R.: Distribution of high-dimensional entanglement via an intra-city free-space link. Nat. Commun. 8, 15971 (2017)

doi: 10.1038/ncomms15971

Kwiat, P.G.: Hyper-entangled states. J. Mod. Opt. 44(11–12), 2173–2184 (1997)

doi: 10.1080/09500349708231877

Souza, R.C., Balthazar, W.F., Huguenin, J.A.O.: Universal quantum gates for path photonic qubit. Quantum Inf. Process. 21, 68 (2022)

doi: 10.1007/s11128-022-03415-x

Solntsev, A.S., Sukhorukov, A.A.: Path-entangled photon sources on nonlinear chips. Rev. Phys. 2, 19–31 (2017)

doi: 10.1016/j.revip.2016.11.003

Balthazar, W.F., Souza, C.E.R., Caetano, D.P., Galvão, E.F., Huguenin, J.A.O., Khoury, A.Z.: Tripartite nonseparability in classical optics. Opt. Lett. 41, 5797–5800 (2016)

doi: 10.1364/OL.41.005797

Li, M., Li, C., Chen, Y., Feng, L.T., Yan, L., Zhang, Q., Bao, J., Liu, B.H., Ren, X.F., Wang, J., Wang, S.: On-chip path encoded photonic quantum Toffoli gate. Photon. Res. 10, 1533–1542 (2022)

doi: 10.1364/PRJ.452539

Babazadeh, A., Erhard, M., Wang, F., Malik, M., Nouroozi, R., Krenn, M., Zeilinger, A.: High-dimensional single-photon quantum gates: concepts and experiments. Phys. Rev. Lett. 119(18), 180510 (2017)

doi: 10.1103/PhysRevLett.119.180510

De Oliveira, A., Walborn, S., Monken, C.: Implementing the Deutsch algorithm with polarization and transverse spatial modes. J. Opt. B Quant. Semiclass. Opt. 7(9), 288 (2005)

doi: 10.1088/1464-4266/7/9/009

Da Lio, B., Cozzolino, D., Biagi, N., Ding, Y., Rottwitt, K., Zavatta, A., Bacco, D., Oxenløwe, L.: Path-encoded high-dimensional quantum communication over a 2-km multicore fiber. npj Quantum Inf. 7, 63 (2021)

doi: 10.1038/s41534-021-00398-y

D’ambrosio, V., Nagali, E., Walborn, S.P., Aolita, L., Slussarenko, S., Marrucci, L., Sciarrino, F.: Complete experimental toolbox for alignment-free quantum communication. Nat. Commun. 3(1), 1 (2012)

Matthews, J., Politi, A., Stefanov, A., O’Brien, J.L.: Manipulation of multiphoton entanglement in waveguide quantum circuits. Nat. Photon. 3, 346–350 (2009)

doi: 10.1038/nphoton.2009.93

Jin, H., Liu, F.M., Xu, P., Xia, J.L., Zhong, M.L., Yuan, Y., Zhou, J.W., Gong, Y.X., Wang, W., Zhu, S.N.: On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits. Phys. Rev. Lett. 113, 103601 (2014)

doi: 10.1103/PhysRevLett.113.103601

Harris, N.C., Grassani, D., Simbula, A., Pant, M., Galli, M., Baehr-Jones, T., Hochberg, M., Englund, D., Bajoni, D., Galland, C.: Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems. Phys. Rev. X 4, 041047 (2014)

Titchener, J.G., Solntsev, A.S., Sukhorukov, A.A.: Generation of photons with all-optically-reconfigurable entanglement in integrated nonlinear waveguides. Phys. Rev. A 92, 033819 (2015)

doi: 10.1103/PhysRevA.92.033819

Solntsev, A.S., Setzpfandt, F., Clark, A.S., Wu, C.W., Collins, M.J., Xiong, C., Schreiber, A., Katzschmann, F., Eilenberger, F., Schiek, R., Sohler, W.: Generation of nonclassical biphoton states through cascaded quantum walks on a nonlinear chip. Phys. Rev. X 4, 031007 (2014)

Schaeff, C., Polster, R., Lapkiewicz, R., Fickler, R., Ramelow, S., Zeilinger, A.: Scalable fiber integrated source for higher-dimensional path-entangled photonic quNits. Opt. Express 20, 16145–16153 (2012)

doi: 10.1364/OE.20.016145

Antonosyan, D.A., Solntsev, A.S., Sukhorukov, A.A.: Effect of loss on photon-pair generation in nonlinear waveguide arrays. Phys. Rev. A 90, 043845 (2014)

doi: 10.1103/PhysRevA.90.043845

Franson, J.D.: Bell inequality for position and time. Phys. Rev. Lett. 62, 2205 (1989)

doi: 10.1103/PhysRevLett.62.2205

Humphreys, P.C., Metcalf, B.J., Spring, J.B., Moore, M., Jin, X.M., Barbieri, M., Kolthammer, W.S., Walmsley, I.A.: Linear optical quantum computing in a single spatial mode. Phys. Rev. Lett. 111, 150501 (2013)

doi: 10.1103/PhysRevLett.111.150501

Donohue, J.M., Agnew, M., Lavoie, J., Resch, K.J.: Coherent ultrafast measurement of time-bin encoded photons. Phys. Rev. Lett. 111, 153602 (2013)

doi: 10.1103/PhysRevLett.111.153602

Ortu, A., Holzäpfel, A., Etesse, J., Afzelius, M.: Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal. npj Quantum Inf. 8, 29 (2022)

doi: 10.1038/s41534-022-00541-3

Kochi, Y., Kurimura, S., Ishi-Hayase, J.: Evaluation of femtosecond time-bin qubits using frequency up-conversion technique. arXive preprint arXiv:2205.06957 [quant-ph] (2022)

Bouchard, F., England, D., Bustard, P.J., Heshami, K., Sussman, B.: Quantum communication with ultrafast time-bin qubits. arXive preprint arXiv:2106.09833 [quant-ph] (2021)

Yu, L., Natarajan, C., Horikiri, T., Langrock, C., Pelc, J.S., Tanner, M.G., Abe, E., Maier, S., Schneider, C., Höfling, S., Kamp, M., Hadfield, R.H., Fejer, M.M., Yamamoto, Y.: Two-photon interference at telecom wavelengths for time-bin-encoded single photons from quantum-dot spin qubits. Nat. Commun. 6, 8955 (2015)

doi: 10.1038/ncomms9955

Tang, G.Z., Sun, S.H., Chen, H., Li, C.Y., Liang, L.M.: Time-bin phase-encoding measurement-device-independent quantum key distribution with four single-photon detectors. Chin. Phys. Lett. 33, 120301 (2016)

doi: 10.1088/0256-307X/33/12/120301

Gündoğan, M., Ledingham, P.M., Kutluer, K., Mazzera, M., de Riedmatten, H.: Solid state spin-wave quantum memory for time-bin qubits. Phys. Rev. Lett. 114, 230501 (2015)

doi: 10.1103/PhysRevLett.114.230501

Marcikic, I., de Riedmatten, H., Tittel, W., Zbinden, H., Gisin, N.: Long-distance teleportation of qubits at telecommunication wavelengths. Nature 421, 509–513 (2003)

doi: 10.1038/nature01376

de Riedmatten, H., Marcikic, I., Tittel, W., Zbinden, H., Collins, D., Gisin, N.: Long distance quantum teleportation in a quantum relay configuration. Phys. Rev. Lett. 92, 047904 (2004)

doi: 10.1103/PhysRevLett.92.047904

Landry, O., van Houwelingen, J.A., Beveratos, A., Zbinden, H., Gisin, N.: Quantum teleportation over the Swisscom telecommunication network. J. Opt. Soc. Am. B 24, 398–403 (2007)

doi: 10.1364/JOSAB.24.000398

Guo, X., Mei, Y., Shengwang, D.: Testing the Bell inequality on frequency-bin entangled photon pairs using time-resolved detection. Optica 4, 388–392 (2017)

doi: 10.1364/OPTICA.4.000388

Nisbet-Jones, P.B.R.: Photonic qubits, qutrits and ququads accurately prepared and delivered on demand. New J. Phys. 15, 053007 (2013)

doi: 10.1088/1367-2630/15/5/053007

Martin, A., Kaiser, F., Vernier, A., Beveratos, A., Scarani, V., Tanzilli, S.: Cross time-bin photonic entanglement for quantum key distribution. Phys. Rev. A 87, 020301(R) (2013)

doi: 10.1103/PhysRevA.87.020301

Harada, K.I., Takesue, H., Fukuda, H., Tsuchizawa, T., Watanabe, T., Yamada, K., Tokura, Y., Itabashi, S.I.: Generation of high-purity entangled photon pairs using silicon wire waveguide. Opt. Express 16, 20368–20373 (2008)

doi: 10.1364/OE.16.020368

Wakabayashi, R., Fujiwara, M., Yoshino, K.I., Nambu, Y., Sasaki, M., Aoki, T.: Time-bin entangled photon pair generation from Si micro-ring resonator. Opt. Express 23, 1103–1113 (2015)

doi: 10.1364/OE.23.001103

Xiong, C., Zhang, X., Mahendra, A., He, J., Choi, D.-Y., Chae, C.J., Marpaung, D., Leinse, A., Heideman, R.G., Hoekman, M., Roeloffzen, C.G.H., Oldenbeuving, R.M., van Dijk, P.W.L., Taddei, C., Leong, P.H.W., Eggleton, B.J.: Compact and reconfigurable silicon nitride time-bin entanglement circuit. Optica 2, 724–727 (2015)

doi: 10.1364/OPTICA.2.000724

He, Y., Ding, X., Su, Z.E., Huang, H.L., Qin, J., Wang, C., Unsleber, S., Chen, C., Wang, H., He, Y.M., Wang, X.L.: Time-bin-encoded boson sampling with a single-photon device. Phys. Rev. Lett. 118, 190501 (2017)

doi: 10.1103/PhysRevLett.118.190501

Motes, K.R., Gilchrist, A., Dowling, J.P., Rohde, P.P.: Scalable boson sampling with time-bin encoding using a loop-based architecture. Phys. Rev. Lett. 113, 120501 (2014)

doi: 10.1103/PhysRevLett.113.120501

Schreiber, A., Cassemiro, K.N., Potoček, V., Gábris, A., Mosley, P.J., Andersson, E., Jex, I., Silberhorn, C.: Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010)

doi: 10.1103/PhysRevLett.104.050502

Regensburger, A., Bersch, C., Hinrichs, B., Onishchukov, G., Schreiber, A., Silberhorn, C., Peschel, U.: Photon propagation in a discrete fiber network: an interplay of coherence and losses. Phys. Rev. Lett. 107, 233902 (2011)

doi: 10.1103/PhysRevLett.107.233902

Schreiber, A.: A 2D quantum walk simulation of two-particle dynamics. Science 336, 55–58 (2012)

doi: 10.1126/science.1218448

Jeong, Y.C., Di Franco, C., Lim, H.T., Kim, M.S., Kim, Y.H.: Experimental realization of a delayed-choice quantum walk. Nat. Commun. 4, 2471 (2013)

doi: 10.1038/ncomms3471

Boutari, J., Feizpour, A., Barz, S., Franco, C.D., Kim, M.S., Kolthammer, W.S., Walmsley, I.A.: Large scale quantum walks by means of optical fiber cavities. J. Opt. 18, 094007 (2016)

doi: 10.1088/2040-8978/18/9/094007

Olislager, L., Cussey, J., Nguyen, A.T., Emplit, P., Massar, S., Merolla, J.M., Huy, K.P.: Frequency-bin entangled photons. Phys. Rev. A 82, 013804 (2010)

doi: 10.1103/PhysRevA.82.013804

Kaneda, F., Suzuki, H., Shimizu, R., Edamatsu, K.: Direct generation of frequency-bin entangled photons via two-period quasi-phase-matched parametric downconversion. Opt. Express 27, 1416 (2019)

doi: 10.1364/OE.27.001416

Rieländer, D., Lenhard, A., Jime’nez Farìas, O., Máttar, A., Cavalcanti, D., Mazzera, M., Acín, A., Riedmatten, H.: Frequency-bin entanglement of ultra-narrow band non-degenerate photon pairs. Quantum Sci. Technol. 3, 014007 (2017)

doi: 10.1088/2058-9565/aa97b6

Lu, H.H., Lukens, J.M., Peters, N.A., Williams, B.P., Weiner, A.M., Lougovski, P.: Quantum interference and correlation control of frequency-bin qubits. Optica 5, 1455–1460 (2018)

doi: 10.1364/OPTICA.5.001455

Imany, P., Jaramillo-Villegas, J.A., Odele, O.D., Han, K., Leaird, D.E., Lukens, J.M., Lougovski, P., Qi, M., Weiner, A.M.: 50-GHz-spaced comb of high-dimensional frequency-bin entangled photons from an on-chip silicon nitride microresonator. Opt. Express 26, 1825 (2018)

doi: 10.1364/OE.26.001825

Reimer, C., Kues, M., Roztocki, P., Wetzel, B., Grazioso, F., Little, B.E., Chu, S.T., Johnston, T., Bromberg, Y., Caspani, L., Moss, D.J., Morandotti, R.: Generation of multiphoton entangled quantum states by means of integrated frequency combs. Science 351, 1176–1180 (2016)

doi: 10.1126/science.aad8532

Zhong, T., Zhou, H., Horansky, R.D., Lee, C., Verma, V.B., Lita, A.E., Restelli, A., Bienfang, J.C., Mirin, R.P., Gerrits, T., Nam, S.W., Marsili, F., Shaw, M.D., Zhang, Z., Wang, L., Englund, D., Wornell, G.W., Shapiro, J.H., Wong, F.N.C.: Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding. New. J. Phys. 17, 022002 (2015)

doi: 10.1088/1367-2630/17/2/022002

Nunn, J., Wright, L.J., Söller, C., Zhang, L., Walmsley, I.A., Smith, B.J.: Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion. Opt. Express 21, 15959–15973 (2013)

doi: 10.1364/OE.21.015959

Hayat, A., Xing, X., Feizpour, A., Steinberg, A.M.: Multidimensional quantum information based on single-photon temporal wavepackets. Opt. Express 20, 29174–29184 (2012)

doi: 10.1364/OE.20.029174

Roslund, J., De Araujo, R.M., Jiang, S., Fabre, C., Treps, N.: Wavelength-multiplexed quantum networks with ultrafast frequency combs. Nat. Photon. 8, 109 (2014)

doi: 10.1038/nphoton.2013.340

Kaiser, F., Aktas, D., Fedrici, B., Lunghi, T., Labonté, L., Tanzilli, S.: Optimal analysis of ultra broadband energy-time entanglement for high bit-rate dense wavelength division multiplexed quantum networks. Appl. Phys. Lett. 108, 231108 (2016)

doi: 10.1063/1.4953785

Campbell, G.T., Pinel, O., Hosseini, M., Ralph, T.C., Buchler, B.C., Lam, P.K.: Configurable unitary transformations and linear logic gates using quantum memories. Phys. Rev. Lett. 113, 063601 (2014)

doi: 10.1103/PhysRevLett.113.063601

Menicucci, N.C., Ma, X., Ralph, T.C.: Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate. Phys. Rev. Lett. 104, 250503 (2010)

doi: 10.1103/PhysRevLett.104.250503

Menicucci, N.C.: Temporal-mode continuous-variable cluster states using linear optics. Phys. Rev. A 83, 062314 (2011)

doi: 10.1103/PhysRevA.83.062314

Yokoyama, S., Ukai, R., Armstrong, S.C., Sornphiphatphong, C., Kaji, T., Suzuki, S., Yoshikawa, J., Yonezawa, H., Menicucci, N.C., Furusawa, A.: Ultra-large-scale continuous-variable cluster states multiplexed in the time domain. Nat. Photon. 7, 982 (2013)

doi: 10.1038/nphoton.2013.287

Chen, M., Menicucci, N.C., Pfister, O.: Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb. Phys. Rev. Lett. 112, 120505 (2014)

doi: 10.1103/PhysRevLett.112.120505

Soudagar, Y., Bussières, F., Berlín, G., Lacroix, S., Fernandez, J.M., Godbout, N.: Cluster-state quantum computing in optical fibers. J. Opt. Soc. Am. B 24, 226–230 (2007)

doi: 10.1364/JOSAB.24.000226

Shalm, L., Hamel, D., Yan, Z., Simon, C., Resch, K.J., Jennewein, T.: Three-photon energy-time entanglement. Nat. Phys. 9, 19–22 (2013)

doi: 10.1038/nphys2492

Hosseini, M., Sparkes, B., Hétet, G., Longdell, J.J., Lam, P.K., Buchler, B.C.: Coherent optical pulse sequencer for quantum applications. Nature 461, 241–245 (2009)

doi: 10.1038/nature08325

Autebert, C., Bruno, N., Martin, A., Lemaitre, A., Carbonell, C.G., Favero, I., Leo, G., Zbinden, H., Ducci, S.: Integrated AlGaAs source of highly indistinguishable and energy-time entangled photons. Optica 3, 143–146 (2016)

doi: 10.1364/OPTICA.3.000143

Reddy, D.V., Raymer, M.G., McKinstrie, C.J.: Efficient sorting of quantum-optical wave packets by temporal-mode interferometry. Opt. Lett. 39, 2924–2927 (2014)

doi: 10.1364/OL.39.002924

Brecht, B., Eckstein, A., Ricken, R., Quiring, V., Suche, H., Sansoni, L., Silberhorn, C.: Demonstration of coherent time-frequency Schmidt mode selection using dispersion-engineered frequency conversion. Phys. Rev. A 90, 030302(R) (2014)

doi: 10.1103/PhysRevA.90.030302

Saglamyurek, E., Sinclair, N., Slater, J.A., Heshami, K., Oblak, D., Tittel, W.: An integrated processor for photonic quantum states using a broadband light-matter interface. New J. Phys. 16, 065019 (2014)

doi: 10.1088/1367-2630/16/6/065019

Huntington, E.H., Ralph, T.C.: Components for optical qubits encoded in sideband modes. Phys. Rev. A 69, 042318 (2004)

doi: 10.1103/PhysRevA.69.042318

Pirandola, S., Laurenza, R., Ottaviani, C., Banchi, L.: Fundamental limits of repeaterless quantum communications. Nat. Commun. 8, 1–15 (2017)

doi: 10.1038/ncomms15043

Duan, L.-M., Lukin, M.D., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001)

doi: 10.1038/35106500

Wilde, M.M., Tomamichel, M., Berta, M.: Converse bounds for private communication over quantum channels. IEEE Trans. Inf. Theory 63, 1792–1817 (2017)

doi: 10.1109/TIT.2017.2648825

Pirandola, S.: End-to-end capacities of a quantum communication network. Commun. Phys. 2, 1–10 (2019)

doi: 10.1038/s42005-019-0147-3

Winnel, M.S., Guanzon, J.J., Hosseinidehaj, N., Ralph, T.C.: Achieving the ultimate end-to-end rates of lossy quantum communication networks. npj Quantum Inf. 8, 129 (2022)

doi: 10.1038/s41534-022-00641-0

Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theoret. Comput. Sci. 560, 7–11 (2014)

doi: 10.1016/j.tcs.2014.05.025

Ekert, A.K.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

doi: 10.1103/PhysRevLett.67.661

Ralph, T.C.: Continuous variable quantum cryptography. Phys. Rev. A 61, 010303 (1999)

doi: 10.1103/PhysRevA.61.010303

Hillery, M.: Quantum cryptography with squeezed states. Phys. Rev. A 61, 022309 (2000)

doi: 10.1103/PhysRevA.61.022309

Wein, S.C., Loredo, J.C., Maffei, M., Hilaire, P., Harouri, A., Somaschi, N., Lemaître, A., Sagnes, I., Lanco, L., Krebs, O., Auffèves, A., Simon, C., Senellart, P., Antón-Solanas, C.: Photon-number entanglement generated by sequential excitation of a two-level atom. Nat. Photon. 16, 374–379 (2022)

doi: 10.1038/s41566-022-00979-z

Santos, A.C., Schneider, C., Bachelard, R., Predojević, A., Antón-Solanas, C.: Multipartite entanglement encoded in the photon-number basis by sequential excitation of a three-level system. Opt. Lett. 48, 6332–6335 (2023)

doi: 10.1364/OL.506403

Arzani, F., Ferraro, A., Parigi, V.: High-dimensional quantum encoding via photon-subtracted squeezed states Phys. Rev. A 99, 022342 (2019)

doi: 10.1103/PhysRevA.99.022342

Ekert, A., Renner, R.: The ultimate physical limits of privacy. Nature 507, 443–447 (2014)

doi: 10.1038/nature13132

Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)

doi: 10.1103/RevModPhys.74.145

Pirandola, S., Andersen, U.L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., Pereira, J.L., Razavi, M., Shamsul Shaari, J., Tomamichel, M., Usenko, V.C., Vallone, G., Villoresi, P., Wallden, P.: Advances in quantum cryptography. Adv. Opt. Photon. 12, 1012–1236 (2020)

doi: 10.1364/AOP.361502

Maring, N., Kutluer, K., Cohen, J., Cristiani, M., Mazzera, M., Ledingham, P.M., Riedmatten, H.: Storage of up-converted telecom photons in a doped crystal. N. J. Phys. 16, 113021 (2014)

doi: 10.1088/1367-2630/16/11/113021

Munro, W.J., Azuma, K., Tamaki, K., Nemoto, K.: Inside quantum repeaters. IEEE J. Sel. Top. Quantum Electron. 21, 78–90 (2015)

doi: 10.1109/JSTQE.2015.2392076

Milburn, G.J.: Photons as qubits. Phys. Scr. T137, 014003 (2009)

doi: 10.1088/0031-8949/2009/T137/014003

Lo, H.-K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012)

doi: 10.1103/PhysRevLett.108.130503

Pirandola, S., Ottaviani, C., Spedalieri, G., Weedbrook, C., Braunstein, S.L., Lloyd, S., Gehring, T., Jacobsen, C.S., Andersen, U.L.: High-rate measurement-device-independent quantum cryptography. Nat. Photon. 9, 397–402 (2015)

doi: 10.1038/nphoton.2015.83

Lucamarini, M., Yuan, Z.L., Dynes, J.F., Shields, A.J.: Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557, 400–403 (2018)

doi: 10.1038/s41586-018-0066-6

Zhong, X., Hu, J., Curty, M., Qian, L., Lo, H.K.: Proof-of-principle experimental demonstration of twin-field type quantum key distribution. Phys. Rev. Lett. 123, 100506 (2019)

doi: 10.1103/PhysRevLett.123.100506

Chen, J.P., Zhang, C., Liu, Y., Jiang, C., Zhang, W., Hu, X.L., Guan, J.Y., Yu, Z.W., Xu, H., Lin, J., Li, M.J., Chen, H., Li, H., You, L., Wang, Z., Wang, X.B., Zhang, Q., Pan, J.W.: Sending-or-not-sending with independent lasers: Secure twin-field quantum key distribution over 509 km. Phys. Rev. Lett. 124, 070501 (2020)

doi: 10.1103/PhysRevLett.124.070501

Liu, H., Jiang, C., Zhu, H.T., Zou, M., Yu, Z.W., Hu, X.L., Xu, H., Ma, S., Han, Z., Chen, J.P., Dai, Y., Tang, S.B., Zhang, W., Li, H., You, L., Wang, Z., Hua, Y., Hu, H., Zhang, H., Zhou, F., Zhang, Q., Wang, X.B., Chen, T.Y., Pan, J.W.: Field test of twin-field quantum key distribution through sending-or-not-sending over 428 km. Phys. Rev. Lett. 126, 250502 (2021)

doi: 10.1103/PhysRevLett.126.250502

Chen, J.P., Zhang, C., Liu, Y., Jiang, C., Zhang, W.J., Han, Z.Y., Ma, S.Z., Hu, X.L., Li, Y.H., Liu, H., Zhou, F., Jiang, H.F., Chen, T.Y., Li, H., You, L.X., Wang, Z., Wang, X.B., Zhang, Q., Pan, J.W.: Twin-field quantum key distribution over a 511 km optical fibre linking two distant metropolitan areas. Nat. Photon. 15, 570–575 (2021)

doi: 10.1038/s41566-021-00828-5

Chen, J.P., Zhang, C., Liu, Y., Jiang, C., Zhao, D.F., Zhang, W.J., Chen, F.X., Li, H., You, L.X., Wang, Z., Chen, Y., Wang, X.B., Zhang, Q., Pan, J.W.: Quantum key distribution over 658 km fiber with distributed vibration sensing. Phys. Rev. Lett. 128, 180502 (2022)

doi: 10.1103/PhysRevLett.128.180502

Erkilic, O., Conlon, L., Shajilal, B., Kish, S., Tserkis, S., Kim, Y., Lam, P., Assad, S.: Surpassing the repeaterless bound with a photon-number encoded measurement-device-independent quantum key distribution protocol. npj Quantum Inf. 9, 29 (2023)

doi: 10.1038/s41534-023-00698-5

Sangouard, N., Simon, C., de Riedmatten, H., Gisin, N.: Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33–80 (2011)

doi: 10.1103/RevModPhys.83.33

Simon, C., de Riedmatten, H., Afzelius, M., Sangouard, N., Zbinden, H., Gisin, N.: Quantum repeaters with photon pair sources and multimode memories. Phys. Rev. Lett. 98, 190503 (2007)

doi: 10.1103/PhysRevLett.98.190503

Dias, J., Winnel, M.S., Hosseinidehaj, N., Ralph, T.C.: Quantum repeater for continuous-variable entanglement distribution. Phys. Rev. A 102, 052425 (2020)

doi: 10.1103/PhysRevA.102.052425

Bussières, F., Clausen, C., Tiranov, A., Korzh, B., Verma, V.B., Nam, S.W., Marsili, F., Ferrier, A., Goldner, P., Herrmann, H., Silberhorn, C., Sohler, W., Afzelius, M., Gisin, N.: Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory. Nat. Photon. 8, 775–778 (2014)

doi: 10.1038/nphoton.2014.215

Stuart, J.S., Hedges, M., Ahlefeldt, R., Sellars, M.: Initialization protocol for efficient quantum memories using resolved hyperfine structure. Phys. Rev. Res. 3, L032054 (2021)

doi: 10.1103/PhysRevResearch.3.L032054

Goebel, A.M., Wagenknecht, C., Zhang, Q., Chen, Y.A., Chen, K., Schmiedmayer, J., Pan, J.W.: Multistage entanglement swapping. Phys. Rev. Lett. 101, 080403 (2008)

doi: 10.1103/PhysRevLett.101.080403

Kaltenbaek, R., Prevedel, R., Aspelmeyer, M., Zeilinger, A.: High-fidelity entanglement swapping with fully independent sources. Phys. Rev. A 79, 040302 (2009)

doi: 10.1103/PhysRevA.79.040302

Li, Z.-D., Zhang, R., Yin, X.F., Liu, L.Z., Hu, Y., Fang, Y.Q., Fei, Y.Y., Jiang, X., Zhang, J., Li, L., Liu, N.L., Xu, F., Chen, Y.A., Pan, J.W.: Experimental quantum repeater without quantum memory. Nat. Photon. 13, 644–648 (2019)

Allen, L., Barnett, S.M., Padgett, M.J.: Optical Angular Momentum. CRC Press (2003)

doi: 10.1887/0750309016

Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992)

doi: 10.1103/PhysRevA.45.8185

Yao, A.M., Padgett, M.J.: Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photon. 3, 161–204 (2011)

doi: 10.1364/AOP.3.000161

Torres, J.P., Torner, L.: Twisted Photons: Applications of Light with Orbital Angular Momentum. Wiley-VCH (2011)

Grier, D.G.: A revolution in optical manipulation. Nature 424, 810–816 (2003)

doi: 10.1038/nature01935

Uribe-Patarroyo, N., Fraine, A., Simon, D.S., Minaeva, O., Sergienko, A.V.: Object identification using correlated orbital angular momentum states. Phys. Rev. Lett. 110, 043601 (2013)

doi: 10.1103/PhysRevLett.110.043601

Wang, J., Yang, J.Y., Fazal, I.M., Ahmed, N., Yan, Y., Huang, H., Ren, Y., Yue, Y., Dolinar, S., Tur, M., Willner, A.E.: Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photon. 6, 488–496 (2012)

doi: 10.1038/nphoton.2012.138

Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001)

doi: 10.1038/35085529

Leach, J., Padgett, M.J., Barnett, S.M., Franke-Arnold, S., Courtial, J.: Measuring the orbital angular momentum of a single photon. Phys. Rev. Lett. 88, 257901 (2002)

doi: 10.1103/PhysRevLett.88.257901

Padgett, M., Bowman, R.: Tweezers with a twist. Nat. Photon. 5, 343–348 (2011)

doi: 10.1038/nphoton.2011.81

Dholakia, K., Čižmár, T.: Shaping the future of manipulation. Nat. Photon. 5, 335–342 (2011)

doi: 10.1038/nphoton.2011.80

Moretti, D., Felinto, D., Tabosa, J. W. R.: Storage and manipulation of orbital angular momentum of light in a cold atomic ensemble. In: CLEO/Europe—EQEC 2009—European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, Munich, Germany, pp. 1–1 (2009)

Liu, X.J., Liu, X., Kwek, L.C., Oh, C.H.: Manipulating atomic states via optical orbital angular-momentum. Front. Phys. China 3, 113–125 (2008)

doi: 10.1007/s11467-008-0024-0

Toyoda, K., Miyamoto, K., Aoki, N., Morita, R., Omatsu, T.: Using optical vortex to control the chirality of twisted metal nanostructures. Nano Lett. 12, 3645–3649 (2012)

doi: 10.1021/nl301347j

Tamburini, F., Anzolin, G., Umbriaco, G., Bianchini, A., Barbieri, C.: Overcoming the Rayleigh criterion limit with optical vortices. Phys. Rev. Lett. 97, 163903 (2006)

doi: 10.1103/PhysRevLett.97.163903

Fürhapter, S., Jesacher, A., Bernet, S., Ritsch-Marte, M.: Spiral interferometry. Opt. Lett. 30, 1953–1955 (2005)

doi: 10.1364/OL.30.001953

Grillo, V., Harvey, T.R., Venturi, F., Pierce, J.S., Balboni, R., Bouchard, F., Carlo Gazzadi, G., Frabboni, S., Tavabi, A.H., Li, Z.A., Dunin-Borkowski, R.E., Boyd, R.W., McMorran, B.J., Karimi, E.: Observation of nanoscale magnetic fields using twisted electron beams. Nat. Commun. 8, 689 (2017)

doi: 10.1038/s41467-017-00829-5

Noguchi, Y., Nakayama, S., Ishida, T., Saitoh, K., Uchida, M.: Efficient measurement of the orbital-angular-momentum spectrum of an electron beam via a Dammann vortex grating. Phys. Rev. Appl. 12, 064062 (2019)

doi: 10.1103/PhysRevApplied.12.064062

Noor, S.K., Yasin, M.N.M., Ismail, A.M., Osman, M.N., Soh, P.J., Ramli, N., Rambe, A.H.: A review of orbital angular momentum vortex waves for the next generation wireless communications. IEEE Access 10, 89465–89484 (2022)

doi: 10.1109/ACCESS.2022.3197653

Lamilla, E., Sacarelo, C., Alvarez-Alvarado, M.S., Pazmino, A., Iza, P.: Optical encoding model based on orbital angular momentum powered by machine learning. Sensors 23, 2755 (2023)

doi: 10.3390/s23052755

Zhu, J., Wang, L., Zhao, S.: Orbital angular momentum multiplexing holography for data storage. IEEE Photon. Technol. Lett. 35, 179–182 (2023)

doi: 10.1109/LPT.2022.3230145

Ding, D.S., Zhang, W., Zhou, Z.Y., Shi, S., Xiang, G.Y., Wang, X.S., Jiang, Y.K., Shi, B.S., Guo, G.C.: Quantum storage of orbital angular momentum entanglement in an atomic ensemble. Phys. Rev. Lett. 114, 050502 (2015)

doi: 10.1103/PhysRevLett.114.050502

Mcmanamon, P., Vedadi, A., Willner, A.E., Choudhary, D., Montifiore, N., Harlev, O.: High capacity and access rate, data storage using laser communications. Opt. Eng. 60, 015105 (2021)

doi: 10.1117/1.OE.60.1.015105

Vaziri, A., Pan, J.-W., Jennewein, T., Weihs, G., Zeilinger, A.: Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum. Phys. Rev. Lett. 91, 227902 (2003)

doi: 10.1103/PhysRevLett.91.227902

Molina-Terriza, G., Torres, J.P., Torner, L.: Twisted photons. Nat. Phys. 3, 305–310 (2007)

doi: 10.1038/nphys607

Nagali, E., Sansoni, L., Sciarrino, F., De Martini, F., Marrucci, L., Piccirillo, B., Karimi, E., Santamato, E.: Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence. Nat. Photon. 3, 720–723 (2009)

doi: 10.1038/nphoton.2009.214

Pors, B.-J., Miatto, F., Hooft, G.W., Eliel, E.R., Woerdman, J.P.: High-dimensional entanglement with orbital-angular-momentum states of light. J. Opt. 13, 064008 (2011)

doi: 10.1088/2040-8978/13/6/064008

Lloyd, S.M., Babiker, M., Thirunavukkarasu, G., Yuan, J.: Electron vortices: beams with orbital angular momentum. Rev. Mod. Phys. 89, 035004 (2017)

doi: 10.1103/RevModPhys.89.035004

Zahidy, M., Liu, Y., Cozzolino, D., Ding, Y., Morioka, T., Oxenløwe, L.K., Bacco, D.: Photonic integrated chip enabling orbital angular momentum multiplexing for quantum communication. Nanophotonics 11(4), 821–827 (2022)

doi: 10.1515/nanoph-2021-0500

Olaleye, T.M., Ribeiro, P.A., Raposo, M.: Generation of photon orbital angular momentum and its application in space division multiplexing. Photonics 10, 664 (2023)

doi: 10.3390/photonics10060664

Wu, C., Kumar, S., Kan, Y., Komisar, D., Wang, Z., Bozhevolnyi, S.I., Ding, F.: Room-temperature on-chip orbital angular momentum single-photon sources. Sci. Adv. 8, eabk3075 (2022)

doi: 10.1126/sciadv.abk3075

Gröblacher, S., Jennewein, T., Vaziris, A., Weihs, G., Zeilinger, A.: Experimental quantum cryptography with qutrits. New J. Phys. 8, 75 (2006)

doi: 10.1088/1367-2630/8/5/075

Langford, N.K., Dalton, R.B., Harvey, M.D., O’Brien, J.L., Pryde, G.J., Gilchrist, A., Bartlett, S.D., White, A.G.: Measuring entangled qutrits and their use for quantum bit commitment. Phys. Rev. Lett. 93, 053601 (2004)

doi: 10.1103/PhysRevLett.93.053601

Molina-Terriza, G., Vaziri, A., Ursin, R., Zeilinger, A.: Experimental quantum coin tossing. Phys. Rev. Lett. 94, 040501 (2005)

doi: 10.1103/PhysRevLett.94.040501

Dada, A.C., Leach, J., Buller, G.S., Padgett, M.J., Andersson, E.: Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nat. Phys. 7, 677–680 (2011)

doi: 10.1038/nphys1996

Bouchard, F., Fickler, R., Boyd, R.W., Karimi, E.: High-dimensional quantum cloning and applications to quantum hacking. Sci. Adv. 3, e1601915 (2017)

doi: 10.1126/sciadv.1601915

Nagali, E., Sansoni, L., Sciarrino, F., De Martini, F., Marrucci, L., Piccirillo, B., Karimi, E., Santamato, E.: Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence. Nat. Photon. 3, 720–723 (2009)

doi: 10.1038/nphoton.2009.214

Hamadou Ibrahim, A., Roux, F.S., McLaren, M., Konrad, T., Forbes, A.: Orbital-angular-momentum entanglement in turbulence. Phys. Rev. A 88, 012312 (2013)

doi: 10.1103/PhysRevA.88.012312

Goyal, S., Boukama-Dzoussi, P., Ghosh, S., Roux, F.S., Konrad, T.: Qudit-Teleportation for photons with linear optics. Sci. Rep. 4, 4543 (2014)

doi: 10.1038/srep04543

Goyal, S.K., Ibrahim, A.H., Roux, F.S., Konrad, T., Forbes, A.: The effect of turbulence on entanglement-based free-space quantum key distribution with photonic orbital angular momentum. J. Opt. 18, 064002 (2016)

doi: 10.1088/2040-8978/18/6/064002

Krenn, M., Handsteiner, J., Fink, M., Fickler, R., Zeilinger, A.: Twisted photon entanglement through turbulent air across Vienna. PNAS 112(46), 14197–14201 (2015)

doi: 10.1073/pnas.1517574112

Hiesmayr, B.C., de Dood, M.J.A., Löffler, W.: Observation of four-photon orbital angular momentum entanglement. Phys. Rev. Lett. 116, 073601 (2016)

doi: 10.1103/PhysRevLett.116.073601

Malik, M., Erhard, M., Huber, M., Krenn, M., Fickler, R., Zeilinger, A.: Multi-photon entanglement in high dimensions. Nat. Photon. 10, 248–252 (2016)

doi: 10.1038/nphoton.2016.12

Erhard, M., Malik, M., Zeilinger, A.: A quantum router for high-dimensional entanglement. Quantum Sci. Technol. 2, 014001 (2017)

doi: 10.1088/2058-9565/aa5917

Fickler, R., Campbell, G., Buchler, B., Lam, P.K., Zeilinger, A.: Quantum entanglement of angular momentum states with quantum numbers up to 10,010. PNAS 113(48), 13642–13647 (2016)

doi: 10.1073/pnas.1616889113

Erhard, M., Malik, M., Krenn, M., et al.: Experimental Greenberger-Horne-Zeilinger entanglement beyond qubits. Nat. Photon. 12, 759–764 (2018)

doi: 10.1038/s41566-018-0257-6

Leonhard, N., Sorelli, G., Shatokhin, V.N., Reinlein, C., Buchleitner, A.: Protecting the entanglement of twisted photons by adaptive optics. Phys. Rev. A 97, 012321 (2018)

doi: 10.1103/PhysRevA.97.012321

Kimble, H.J.: The quantum internet. Nature 453, 1023–1030 (2008)

doi: 10.1038/nature07127

Hamilton, C.S., Gábris, A., Jex, I., Barnett, S.M.: Quantum walk with a four-dimensional coin. New J. Phys. 13, 013015 (2011)

doi: 10.1088/1367-2630/13/1/013015

Innocenti, L., Majury, H., Giordani, T., Spagnolo, N., Sciarrino, F., Paternostro, M., Ferraro, A.: Quantum state engineering using one-dimensional discrete-time quantum walks. Phys. Rev. A 96, 062326 (2017)

doi: 10.1103/PhysRevA.96.062326

Cardano, F., Massa, F., Qassim, H., Karimi, E., Slussarenko, S., Paparo, D., de Lisio, C., Sciarrino, F., Santamato, E., Boyd, R.W., Marrucci, L.: Quantum walks and wavepacket dynamics on a lattice with twisted photons. Sci. Adv. 1, e1500087 (2015)

doi: 10.1126/sciadv.1500087

Cardano, F., Maffei, M., Massa, F., Piccirillo, B., de Lisio, C., De Filippis, G., Cataudella, V., Santamato, E., Marrucci, L.: Statistical moments of quantum-walk dynamics reveal topological quantum transitions. Nat. Commun. 7, 11439 (2016)

doi: 10.1038/ncomms11439

Zhang, P., Liu, B.H., Liu, R.F., Li, H.R., Li, F.L., Guo, G.C.: Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons. Phys. Rev. A 81, 052322 (2010)

doi: 10.1103/PhysRevA.81.052322

Cardano, F., D’Errico, A., Dauphin, A., Maffei, M., Piccirillo, B., de Lisio, C., De Filippis, G., Cataudella, V., Santamato, E., Marrucci, L., Lewenstein, M., Massignan, P.: Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons. Nat. Commun. 8, 15516 (2017)

doi: 10.1038/ncomms15516

Erhard, M., Fickler, R., Krenn, M., Zeilinger, A.: Twisted photons: new quantum perspectives in high dimensions. Light Sci. Appl. 7, 17146 (2018)

doi: 10.1038/lsa.2017.146

Vallone, G., D’Ambrosio, V., Sponselli, A., Slussarenko, S., Marrucci, L., Sciarrino, F., Villoresi, P.: Free-space quantum key distribution by rotation-invariant twisted photons. Phys. Rev. Lett. 113, 060503 (2014)

doi: 10.1103/PhysRevLett.113.060503

Mirhosseini, M., Magaña-Loaiza, O.S., O’Sullivan, M.N., Rodenburg, B., Malik, M., Lavery, M.P.J., Padgett, M.J., Gauthier, D.J., Boyd, R.W.: High-dimensional quantum cryptography with twisted light. New J. Phys. 17, 033033 (2015)

doi: 10.1088/1367-2630/17/3/033033

Lei, T., Zhang, M., Li, Y., Jia, P., Liu, G.N., Xu, X., Li, Z., Min, C., Lin, J., Yu, C., Niu, H., Yuan, X.: Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light Sci. Appl. 4, e257 (2015)

doi: 10.1038/lsa.2015.30

Wang, F.X., Chen, W., Yin, Z.Q., Wang, S., Guo, G.C., Han, Z.F.: Erratum: scalable orbital-angular-momentum sorting without destroying photon states. Phys. Rev. A 95, 019903 (2017)

doi: 10.1103/PhysRevA.95.019903

Pan, Z., Cai, J., Wang, C.: Quantum key distribution with high order Fibonacci-like orbital angular momentum states. Int. J. Theor. Phys. 56, 2622–2634 (2017)

doi: 10.1007/s10773-017-3418-3

Sit, A., Bouchard, F., Fickler, R., Gagnon-Bischoff, J., Larocque, H., Heshami, K., Elser, D., Peuntinger, C., Günthner, K., Heim, B., Marquardt, C.: High-dimensional intracity quantum cryptography with structured photons. Optica 4, 1006–1010 (2017)

doi: 10.1364/OPTICA.4.001006

Mafu, M., Dudley, A., Goyal, S., Giovannini, D., McLaren, M., Padgett, M.J., Konrad, T., Petruccione, F., Lütkenhaus, N., Forbes, A.: Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys. Rev. A 88, 032305 (2013)

doi: 10.1103/PhysRevA.88.032305

D’Ambrosio, V., Spagnolo, N., Del Re, L., Slussarenko, S., Li, Y., Kwek, L.C., Marrucci, L., Walborn, S.P., Aolita, L., Sciarrino, F.: Photonic polarization gears for ultra-sensitive angular measurements. Nat. Commun. 4, 2432 (2013)

doi: 10.1038/ncomms3432

Jha, A.K., Agarwal, G.S., Boyd, R.W.: Supersensitive measurement of angular displacements using entangled photons. Phys. Rev. A 83, 053829 (2011)

doi: 10.1103/PhysRevA.83.053829

Karimi, E., Piccirillo, B., Nagali, E., Marrucci, L., Santamato, E.: Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned [Formula: see text]-plates. Appl. Phys. Lett. 94, 231124 (2009)

doi: 10.1063/1.3154549

Zhang, W., Qi, Q., Zhou, J., Chen, L.: Mimicking faraday rotation to sort the orbital angular momentum of light. Phys. Rev. Lett. 112, 153601 (2014)

doi: 10.1103/PhysRevLett.112.153601

Wang, X.L., Cai, X.D., Su, Z.E., Chen, M.C., Wu, D., Li, L., Liu, N.L., Lu, C.Y., Pan, J.W.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516–519 (2015)

doi: 10.1038/nature14246

Goyal, S., Konrad, T.: Teleporting photonic qudits using multimode quantum scissors. Sci. Rep. 3, 3548 (2013)

doi: 10.1038/srep03548

Ding, D.S., Zhou, Z.Y., Shi, B.S., Guo, G.C.: Single-photon-level quantum image memory based on cold atomic ensembles. Nat. Commun. 4, 2527 (2013)

doi: 10.1038/ncomms3527

Cai, X., Wang, J., Strain, M. J., Johnson-Morris, B., Zhu, J., Sorel, M., O'Brien, J., Thompson, M., Yu, S.: Integrated compact optical vortex beam emitters. Science 338, 363–366 (2012)

doi: 10.1126/science.1226528

Alonso, J.R.G., Brun, T.A.: Protecting orbital-angular-momentum photons from decoherence in a turbulent atmosphere. Phys. Rev. A 88, 022326 (2013)

doi: 10.1103/PhysRevA.88.022326

Alonso, J.R.G., Brun, T.: Recovering quantum information in orbital angular momentum of photons by adaptive optics. arXive preprints arXiv:1612.02552 [quant-ph] (2016)

Padgett, M.J., Miatto, F.M., Lavery, M.P.J., Zeilinger, A., Boyd, R.W.: Divergence of an orbital-angular-momentum-carrying beam upon propagation. New J. Phys. 17, 023011 (2015)

doi: 10.1088/1367-2630/17/2/023011

Farías, O., D’Ambrosio, V., Taballione, C., Bisesto, F., Slussarenko, S., Aolita, L., Marrucci, L., Walborn, S.P., Sciarrino, F.: Resilience of hybrid optical angular momentum qubits to turbulence. Sci. Rep. 5, 8424 (2015)

doi: 10.1038/srep08424

Lvovsky, A.I., Sanders, B.C., Tittel, W.: Optical quantum memory. Nat. Photon. 3, 706–714 (2009)

doi: 10.1038/nphoton.2009.231

Inoue, R., Kanai, N., Yonehara, T., Miyamoto, Y., Koashi, M., Kozuma, M.: Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon. Phys. Rev. A 74, 053809 (2006)

doi: 10.1103/PhysRevA.74.053809

Pugatch, R., Shuker, M., Firstenberg, O., Ron, A., Davidson, N.: Topological stability of optical vortices. Phys. Rev. Lett. 98, 203601 (2007)

doi: 10.1103/PhysRevLett.98.203601

Moretti, D., Felinto, D., Tabosa, J.W.R.: Collapses and revivals of stored orbital angular momentum of light in a cold-atom ensemble. Phys. Rev. A 79, 023825 (2009)

doi: 10.1103/PhysRevA.79.023825

Veissier, L., Nicolas, A., Giner, L., Maxein, D., Sheremet, A.S., Giacobino, E., Laurat, J.: Reversible optical memory for twisted photons. Opt. Lett. 38, 712–714 (2013)

doi: 10.1364/OL.38.000712

Ding, D.S., Zhou, Z.Y., Shi, B.S., Guo, G.G.: Single-photon level quantum image memory based on cold atomic ensembles. Nat. Commun. 4, 2527 (2013)

doi: 10.1038/ncomms3527

Nicolas, A., Veissier, L., Giner, L., Giacobino, E., Maxein, D., Laurat, J.: A quantum memory for orbital angular momentum photonic qubits. Nat. Photon. 8, 234–238 (2014)

doi: 10.1038/nphoton.2013.355

Zhou, Z.Y., Li, Y., Ding, D.S., Zhang, W., Shi, S., Shi, B.S., Guo, G.C.: Orbital angular momentum photonic quantum interface. Light Sci. Appl. 5, e16019 (2016)

doi: 10.1038/lsa.2016.19

Choi, C.Q.: Two of world’s biggest quantum computers made in China: Quantum computers Zuchongzi and Jiuzhang 2.0 may both display "quantum primacy" over classical computers. IEEE Spectrum (2021). Available at the website of spectrum.ieee.org/quantum-computing-china

Chen, Y.H., Cho, C.H., Yuan, W., Ma, Y., Wen, K., Chang, C.R.: Photonic quantum computers enlighten the world: a review of their development, types, and applications. IEEE Nanatechnol. Mag. 16(4), 4–9 (2022)

doi: 10.1109/MNANO.2022.3175382

Bartlett, B., Dutt, A., Fan, S.: Deterministic photonic quantum computation in a synthetic time dimension. Optica 8, 1515–1523 (2021)

doi: 10.1364/OPTICA.424258

Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41, 303 (1999)

doi: 10.1137/S0036144598347011

Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997)

doi: 10.1103/PhysRevLett.79.325

Pfister, O.: Continuous-variable quantum computing in the quantum optical frequency comb. J. Phys. B: At. Mol. Opt. Phys. 53, 012001 (2019)

doi: 10.1088/1361-6455/ab526f

Fukui, K., Takeda, S.: Building a large-scale quantum computer with continuous-variable optical technologies. J. Phys. B: At. Mol. Opt. Phys. 55, 012001 (2022)

doi: 10.1088/1361-6455/ac489c

Yoshikawa, J., Yokoyama, S., Kaji, T., Sornphiphatphong, C., Shiozawa, Y., Makino, K., Furusawa, A.: Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing. APL Photon. 1(6), 060801 (2016)

doi: 10.1063/1.4962732

Asavanant, W., Shiozawa, Y., Yokoyama, S., Charoensombutamon, B., Emura, H., Alexander, R.N., Takeda, S., Yoshikawa, J.I., Menicucci, N.C., Yonezawa, H., Furusawa, A.: Generation of time-domain-multiplexed two-dimensional cluster state. Science 366(6463), 373–376 (2019)

doi: 10.1126/science.aay2645

Larsen, M.V., Guo, X., Breum, C.R., Neergaard-Nielsen, J.S., Andersen, U.L.: Deterministic generation of a two-dimensional cluster state. Science 366, 369 (2019)

doi: 10.1126/science.aay4354

Larsen, M.V., Guo, X., Breum, C.R., Neergaard-Nielsen, J.S., Andersen, U.L.: Deterministic multi-mode gates on a scalable photonic quantum computing platform. Nat. Phys. 17, 1018–1023 (2021)

doi: 10.1038/s41567-021-01296-y

Asavanant, W., Charoensombutamon, B., Yokoyama, S., Ebihara, T., Nakamura, T., Alexander, R.N., Endo, M., Yoshikawa, J.I., Menicucci, N.C., Yonezawa, H., Furusawa, A.: Time-domain-multiplexed measurement-based quantum operations with 25-mHz clock frequency. Phys. Rev. Appl. 16, 034005 (2021)

doi: 10.1103/PhysRevApplied.16.034005

Pysher, M., Miwa, Y., Shahrokhshahi, R., Bloomer, R., Pfister, O.: Parallel generation of quadripartite cluster entanglement in the optical frequency comb. Phys. Rev. Lett. 107, 030505 (2011)

doi: 10.1103/PhysRevLett.107.030505

Cai, Y., Roslund, J., Ferrini, G., Arzani, F., Xu, X., Fabre, C., Treps, N.: Multimode entanglement in reconfigurable graph states using optical frequency combs. Nat. Commun. 8, 15645 (2017)

doi: 10.1038/ncomms15645

Grimsmo, A.L., Blais, A.: Squeezing and quantum state engineering with Josephson travelling wave amplifiers. npj Quantum Inf. 3, 20 (2017)

doi: 10.1038/s41534-017-0020-8

Schmidt, M., Ludwig, M., Marquardt, F.: Optomechanical circuits for nanomechanical continuous variable quantum state processing. New J. Phys. 14, 125005 (2012)

doi: 10.1088/1367-2630/14/12/125005

Houhou, O., Aissaoui, H., Ferraro, A.: Generation of cluster states in optomechanical quantum systems. Phys. Rev. A 92, 063843 (2015)

doi: 10.1103/PhysRevA.92.063843

Ikeda, Y., Yamamoto, N.: Deterministic generation of gaussian pure states in a quasilocal dissipative system. Phys. Rev. A 87, 033802 (2013)

doi: 10.1103/PhysRevA.87.033802

Motes, K.R., Baragiola, B.Q., Gilchrist, A., Menicucci, N.C.: Encoding qubits into oscillators with atomic ensembles and squeezed light. Phys. Rev. A 95, 053819 (2017)

doi: 10.1103/PhysRevA.95.053819

Flühmann, C., Negnevitsky, V., Marinelli, M., Home, J.P.: Sequential modular position and momentum measurements of a trapped ion mechanical oscillator. Phys. Rev. X 8, 02100110 (2018)

Flühmann, C., Nguyen, T.L., Marinelli, M., Negnevitsky, V., Mehta, K., Home, J.: Encoding a qubit in a trapped-ion mechanical oscillator. Nature 566, 513 (2019)

doi: 10.1038/s41586-019-0960-6

Pegg, D., Barnett, S.: Phase properties of the quantized single-mode electromagnetic field. Phys. Rev. A 39, 1665 (1989)

doi: 10.1103/PhysRevA.39.1665

Chuang, I.L., Leung, D.W., Yamamoto, Y.: Bosonic quantum codes for amplitude damping. Phys. Rev. A 56, 1114 (1997)

doi: 10.1103/PhysRevA.56.1114

Albert, V.V., Noh, K., Duivenvoorden, K., Young, D.J., Brierley, R., Reinhold, P., Vuillot, C., Li, L., Shen, C., Girvin, S., Terhal, B.M., Jiang, L.: Performance and structure of single-mode bosonic codes. Phys. Rev. A 97, 032346 (2018)

doi: 10.1103/PhysRevA.97.032346

Grimsmo, A.L., Combes, J., Baragiola, B.Q.: Quantum computing with rotation-symmetric bosonic codes. Phys. Rev. X 10, 011058 (2020)

Cochrane, P.T., Milburn, G.J., Munro, W.J.: Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Phys. Rev. A 59, 2631 (1999)

doi: 10.1103/PhysRevA.59.2631

Michael, M.H., Silveri, M., Brierley, R., Albert, V.V., Salmilehto, J., Jiang, L., Girvin, S.M.: New class of quantum error-correcting codes for a bosonic mode. Phys. Rev. X 6, 031006 (2016)

Gottesman, D., Kitaev, A., Preskill, J.: Encoding a qubit in an oscillator. Phys. Rev. A 64(1), 012310 (2001)

doi: 10.1103/PhysRevA.64.012310

Menicucci, N.C.: Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. Phys. Rev. Lett. 112, 120504 (2014)

doi: 10.1103/PhysRevLett.112.120504

Fukui, K., Tomita, A., Okamoto, A.: Analog quantum error correction with encoding a qubit into an oscillator. Phys. Rev. Lett. 119, 180507 (2017)

doi: 10.1103/PhysRevLett.119.180507

Fukui, K., Tomita, A., Okamoto, A., Fujii, K.: High-threshold fault-tolerant quantum computation with analog quantum error correction. Phys. Rev. X 8, 021054 (2018)

Douce, T., Markham, D., Kashefi, E., Van Loock, P., Ferrini, G.: Probabilistic fault-tolerant universal quantum computation and sampling problems in continuous variables. Phys. Rev. A 99, 012344 (2019)

doi: 10.1103/PhysRevA.99.012344

Vuillot, C., Asasi, H., Wang, Y., Pryadko, L.P., Terhal, B.M.: Quantum error correction with the toric Gottesman-Kitaev-Preskill code. Phys. Rev. A 99, 032344 (2019)

doi: 10.1103/PhysRevA.99.032344

Baragiola, B.Q., Pantaleoni, G., Alexander, R.N., Karanjai, A., Menicucci, N.C.: All-gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code. Phys. Rev. Lett. 123, 200502 (2019)

doi: 10.1103/PhysRevLett.123.200502

Shi, Y., Chamberland, C., Cross, A.: Fault-tolerant preparation of approximate GKP states. New J. Phys. 21, 093007 (2019)

doi: 10.1088/1367-2630/ab3a62

Walshe, B.W., Mensen, L.J., Baragiola, B.Q., Menicucci, N.C.: Robust fault tolerance for continuous-variable cluster states with excess antisqueezing. Phys. Rev. A 100, 010301 (2019)

doi: 10.1103/PhysRevA.100.010301

Pantaleoni, G., Baragiola, B.Q., Menicucci, N.C.: Modular bosonic subsystem codes. Phys. Rev. Lett. 125, 040501 (2020)

doi: 10.1103/PhysRevLett.125.040501

Walshe, B.W., Baragiola, B.Q., Alexander, R.N., Menicucci, N.C.: Continuous-variable gate teleportation and bosonic-code error correction. Phys. Rev. A 102, 062411 (2020)

doi: 10.1103/PhysRevA.102.062411

Pantaleoni, G., Baragiola, B.Q., Menicucci, N.C.: Subsystem analysis of continuous-variable resource states. Phys. Rev. A 104, 012430 (2021)

doi: 10.1103/PhysRevA.104.012430

Grimsmo, A.L., Puri, S.: Quantum error correction with the Gottesman-Kitaev-Preskill code. PRX Quantum 2, 020101 (2021)

doi: 10.1103/PRXQuantum.2.020101

Fukui, K., Tomita, A., Okamoto, A.: Tracking quantum error correction. Phys. Rev. A 98, 022326 (2018)

doi: 10.1103/PhysRevA.98.022326

Noh, K., Chamberland, C.: Fault-tolerant bosonic quantum error correction with the surface-Gottesman-Kitaev-Preskill code. Phys. Rev. A 101, 012316 (2020)

doi: 10.1103/PhysRevA.101.012316

Noh, K., Girvin, S., Jiang, L.: Encoding an oscillator into many oscillators. Phys. Rev. Lett. 125, 080503 (2020)

doi: 10.1103/PhysRevLett.125.080503

Yamasaki, H., Fukui, K., Takeuchi, Y., Tani, S., Koashi, M.: Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-gaussian implementation with gottesman-kitaev-preskill code. arXiv preprint arXiv:2006.05416 (2020)

Noh, K., Chamberland, C., Brandão, F. G.: Low overhead fault-tolerant quantum error correction with the surface-gkp code. arXiv preprint arXiv:2103.06994 (2021)

Tzitrin, I., Matsuura, T., Alexander, R.N., Dauphinais, G., Bourassa, J.E., Sabapathy, K.K., Menicucci, N.C., Dhand, I.: Fault-tolerant quantum computation with static linear optics. PRX Quantum 2, 040353 (2021)

doi: 10.1103/PRXQuantum.2.040353

Seshadreesan, K.P., Dhara, P., Patil, A., Jiang, L., Guha, S.: Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits. Phys. Rev. A 105, 052416 (2022)

doi: 10.1103/PhysRevA.105.052416

Stafford, M. P., Menicucci, N. C.: Biased gottesman-kitaev-preskill repetition code. arXiv preprint arXiv:2212.11397 (2022)

Takeda, S., Furusawa, A.: Universal quantum computing with measurement-induced continuous-variable gate sequence in a loop-based architecture. Phys. Rev. Lett. 119, 120504 (2017)

doi: 10.1103/PhysRevLett.119.120504

Alexander, R.N., Yokoyama, S., Furusawa, A., Menicucci, N.C.: Universal quantum computation with temporal-mode bilayer square lattices. Phys. Rev. A 97, 032302 (2018)

doi: 10.1103/PhysRevA.97.032302

Fukui, K., Alexander, R.N., van Loock, P.: All-optical long-distance quantum communication with Gottesman-Kitaev-Preskill qubits. Phys. Rev. Res. 3, 033118 (2021)

doi: 10.1103/PhysRevResearch.3.033118

Rozpędek, F., Noh, K., Xu, Q., Guha, S., Jiang, L.: Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes. npj Quantum Inf. 7, 102 (2021)

doi: 10.1038/s41534-021-00438-7

Terhal, B., Weigand, D.: Encoding a qubit into a cavity mode in circuit QED using phase estimation. Phys. Rev. A 93, 012315 (2016)

doi: 10.1103/PhysRevA.93.012315

Campagne-Ibarcq, P., Eickbusch, A., Touzard, S., Zalys-Geller, E., Frattini, N.E., Sivak, V.V., Reinhold, P., Puri, S., Shankar, S., Schoelkopf, R.J., Frunzio, L., Mirrahimi, M., Devoret, M.H.: Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 584, 368 (2020)

doi: 10.1038/s41586-020-2603-3

Pirandola, S., Mancini, S., Vitali, D., Tombesi, P.: Constructing finite-dimensional codes with optical continuous variables. Europhys. Lett. 68, 323 (2004)

doi: 10.1209/epl/i2004-10203-9

Pirandola, S., Mancini, S., Vitali, D., Tombesi, P.: Continuous variable encoding by ponderomotive interaction. Eur. Phys. J. D-Atomic Mol. Opt. Plasma. Phys. 37, 283 (2006)

Pirandola, S., Mancini, S., Vitali, D., Tombesi, P.: Generating continuous variable quantum codewords in the near-field atomic lithography. J. Phys. B: At. Mol. Opt. Phys. 39, 997 (2006)

doi: 10.1088/0953-4075/39/4/023

Eaton, M., Nehra, R., Pfister, O.: Non-Gaussian and Gottesman-Kitaev-Preskill state preparation by photon catalysis. New J. Phys. 21, 113034 (2019)

doi: 10.1088/1367-2630/ab5330

Su, D., Myers, C.R., Sabapathy, K.K.: Conversion of gaussian states to non-gaussian states using photon-number-resolving detectors. Phys. Rev. A 100, 052301 (2019)

doi: 10.1103/PhysRevA.100.052301

Arrazola, J.M., Bromley, T.R., Izaac, J., Myers, C.R., Brádler, K., Killoran, N.: Machine learning method for state preparation and gate synthesis on photonic quantum computers. Quantum Sci. Technol. 4, 024004 (2019)

doi: 10.1088/2058-9565/aaf59e

Tzitrin, I., Bourassa, J.E., Menicucci, N.C., Sabapathy, K.K.: Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes. Phys. Rev. A 101, 032315 (2020)

doi: 10.1103/PhysRevA.101.032315

Lin, C.Y., Su, W.C., Wu, S.T.: Encoding qubits into harmonic-oscillator modes via quantum walks in phase space. Quantum Inf. Process. 19, 1 (2020)

doi: 10.1007/s11128-020-02775-6

Hastrup, J., Andersen, U. L.: Generation of optical Gottesman-Kitaev-Preskil states with cavity QED. arXiv preprint arXiv:2104.07981 (2021)

Fukui, K., Endo, M., Asavanant, W., Sakaguchi, A., Yoshikawa, J., Furusawa, A.: Generating the gottesman-kitaev-preskill qubit using a cross-kerr interaction between squeezed light and fock states in optics. Phys. Rev. A 105, 022436 (2022)

doi: 10.1103/PhysRevA.105.022436

Fukui, K., Menicucci, N. C.: An efficient, concatenated, bosonic code for additive gaussian noise. arXiv preprint arXiv:2102.01374 (2021)

Takase, K., Fukui, K., Kawasaki, A., Asavanant, W., Endo, M., Yoshikawa, J., van Loock, P., Furusawa, A.: Gaussian breeding for encoding a qubit in propagating light. arXiv preprint arXiv:2212.05436 (2022)

Fukui, K.: High-threshold fault-tolerant quantum computation with the Gottesman-Kitaev-Preskill qubit under noise in an optical setup. Phys. Rev. A 107, 052414 (2023)

doi: 10.1103/PhysRevA.107.052414

Fluhmann, C., Home, J.P.: Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator. Phys. Rev. Lett. 125, 043602 (2020)

doi: 10.1103/PhysRevLett.125.043602

de Neeve, B., Nguyen, T. L., Behrle, T., Home, J.: Error correction of a logical grid state qubit by dissipative pumping. arXiv preprint arXiv:2010.09681 [quant-ph] (2020)

Larsen, M. V., Chamberland, C., Noh, K., Neergaard-Nielsen, J. S., Andersen, U. L.: A fault-tolerant continuous-variable measurement-based quantum computation architecture. arXiv preprint arXiv:2101.03014 (2021)

Xue, X., D’Anjou, B., Watson, T.F., Ward, D.R., Savage, D.E., Lagally, M.G., Friesen, M., Coppersmith, S.N., Eriksson, M.A., Coish, W.A., Vandersypen, L.M.K.: Repetitive quantum nondemolition measurement and soft decoding of a silicon spin qubit. Phys. Rev. X 10, 021006 (2020)

D’Anjou, B.: Generalized figure of merit for qubit read-out. Phys. Rev. A 103, 042404 (2021)

doi: 10.1103/PhysRevA.103.042404

Aharonovich, I., Englund, D., Toth, M.: Solid-state single-photon emitters. Nat. Photon. 10(10), 631–641 (2016)

doi: 10.1038/nphoton.2016.186

Meyer-Scott, E., Silberhorn, C., Migdall, A.: Single-photon sources: approaching the ideal through multiplexing. Rev. Sci. Instrum. 91, 041101 (2020)

doi: 10.1063/5.0003320

Thomas, S., Senellart, P.: The race for the ideal single-photon source is on. Nat. Nanotechnol. 16, 367–368 (2021)

doi: 10.1038/s41565-021-00851-1

Mandel, L., Wolf, E.: Optical Coherence and Quantum Optics. Cambridge University Press (1995)

doi: 10.1017/CBO9781139644105

Grynberg, G., Aspect, A., Fabre, C.: Introduction to Quantum Optics. Cambridge University Press (2010)

doi: 10.1017/CBO9780511778261

Mansuripur, M., Wright, E.M.: Fundamental properties of beam-splitters in classical and quantum optics. Am. J. Phys. 91, 298–306 (2023)

doi: 10.1119/5.0102760

Soref, R., Bennett, B.: Electrooptical effects in silicon. IEEE J. Quantum Electron. 23, 123–129 (1987)

doi: 10.1109/JQE.1987.1073206

Nedeljkovic, M., Soref, R., Mashanovich, G.Z.: Free-carrier electrorefraction and electroabsorption modulation predictions for silicon over the 1–14-μm infrared wavelength range. IEEE Photon. J. 3, 1171–1180 (2011)

doi: 10.1109/JPHOT.2011.2171930

Liu, S., Feng, J., Tian, Y., Zhao, H., Jin, L., Ouyang, B., Zhu, J., Guo, J.: Thermo-optic phase shifters based on silicon-on-insulator platform: state-of-the-art and a review. Front. Optoelectron. 15, 9 (2022)

doi: 10.1007/s12200-022-00012-9

Wu, K., Guo, C., Wang, H., Zhang, X., Wang, J., Chen, J.: All-optical phase shifter and switch near 1550 nm using tungsten disulfide (WS2) deposited tapered fiber. Opt. Express 25, 17639–17649 (2017)

doi: 10.1364/OE.25.017639

Supradeepa, V.R., Long, C.M., Wu, R., Ferdous, F., Hamidi, E., Leaird, D.E., Weiner, A.M.: Comb-based radiofrequency photonic filters with rapid tunability and high selectivity. Nat. Photon. 6, 186–194 (2012)

doi: 10.1038/nphoton.2011.350

Marpaung, D., Yao, J., Capmany, J.: Integrated microwave photonics. Nat. Photon. 13, 80–90 (2019)

doi: 10.1038/s41566-018-0310-5

Fandiño, J.S., Muñoz, P., Doménech, D., Capmany, J.: A monolithic integrated photonic microwave filter. Nat. Photon. 11, 124–129 (2016)

doi: 10.1038/nphoton.2016.233

Eggleton, B.J., Poulton, C.G., Rakich, P.T., Steel, M.J., Bahl, G.: Brillouin integrated photonics. Nat. Photon. 13, 664–677 (2019)

doi: 10.1038/s41566-019-0498-z

Greiner, M., Mandel, O., Esslinger, T., Hänsch, T.W., Bloch, I.: Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002)

doi: 10.1038/415039a

Hu, J., Urvoy, A., Vendeiro, Z., Crépel, V., Chen, W., Vuletić, V.: Creation of a Bose-condensed gas of 87Rb by laser cooling. Science 358, 1078–1080 (2017)

doi: 10.1126/science.aan5614

Yoo, S.J.B.: Wavelength conversion technologies for WDM network applications. J. Light. Technol. 14, 955–966 (1996)

doi: 10.1109/50.511595

Lukens, J.M., Lu, H.H., Qi, B., Lougovski, P., Weiner, A.M., & Williams, B.P.: All-optical frequency processor for networking applications. J. Light. Technol. 38, 1678–1687 (2020)

doi: 10.1109/JLT.2019.2953363

Mueller, T., Xia, F., Avouris, P.: Graphene photodetectors for high-speed optical communications. Nat. Photon. 4(5), 297–301 (2010)

doi: 10.1038/nphoton.2010.40

Li, G., Wang, Y., Huang, L., Sun, W.: Research progress of high-sensitivity perovskite photodetectors: a review of photodetectors: noise, structure, and materials. ACS Appl. Electron. Mater. 4(4), 1485–1505 (2022)

doi: 10.1021/acsaelm.1c01349

Konstantatos, G.: Current status and technological prospect of photodetectors based on two-dimensional materials. Nat. Commun. 9, 5266 (2018)

doi: 10.1038/s41467-018-07643-7

Peumans, P., Bulovic, V., Forrest, S.R.: Efficient, high-bandwidth organic multilayer photodetectors. Appl. Phys. Lett. 76, 3855–3857 (2000)

doi: 10.1063/1.126800

Baeg, K.J., Binda, M., Natali, D., Caironi, M., Noh, Y.Y.: Organic light detectors: photodiodes and phototransistors. Adv. Mater. 25, 4267–95 (2013)

doi: 10.1002/adma.201204979

Sarto, A.W., Van Zeghbroeck, B.J.: Photocurrents in a metal-semiconductor-metal photodetector. IEEE J. Quantum Electron. 33(12), 2188–2194 (1997)

doi: 10.1109/3.644100

Yang, T., Shou, C., Xu, L., Tran, J., He, Y., Li, Y., Wei, P., Liu, J.: Metal-semiconductor-metal photodetectors based on [Formula: see text] thin films. ACS Appl. Electron. Mater. 5(4), 2122–2130 (2023)

doi: 10.1021/acsaelm.3c00035

Averin, S.V., Kotov, V.M.: High spectral selectivity metal-semiconductor-metal photodetector. Opt. Quant. Electron. 55, 37 (2023)

doi: 10.1007/s11082-022-04085-w

Yoo, H., Lee, I.S., Jung, S., Rho, S.M., Kang, B.H., Kim, H.J.: A review of phototransistors using metal oxide semiconductors: research progress and future directions. Adv. Mater. 33(47), 2006091 (2021)

doi: 10.1002/adma.202006091

Glover, A.M.: A review of the development of sensitive phototubes. Proc. IRE 29(8), 413–423 (1941)

doi: 10.1109/JRPROC.1941.230984

Ekert, A.: Quantum interferometers as quantum computers. Phys. Scr. 1998, 218 (1998)

doi: 10.1238/Physica.Topical.076a00218

Spagnolo, N., Aparo, L., Vitelli, C., Crespi, A., Ramponi, R., Osellame, R., Mataloni, P., Sciarrino, F.: Quantum interferometry with three-dimensional geometry. Sci. Rep. 2, 862 (2012)

doi: 10.1038/srep00862

Tan, S.H., Rohde, P.P.: The resurgence of the linear optics quantum interferometer—recent advances and applications. Rev. Phys. 4, 100030 (2019)

doi: 10.1016/j.revip.2019.100030

Chen, Y., Hong, L., Chen, L.: Quantum interferometric metrology with entangled photons. Front. Phys. 10, 892519 (2022)

doi: 10.3389/fphy.2022.892519

Priti, R.B., Liboiron-Ladouceur, O.: A broadband rearrangeable nonblocking MZI-based thermo-optic O-band switch in the silicon-on-insulator. In: Advanced Photonics 2017 (IPR, NOMA, Sensors, Networks, SPPCom, PS). Optical Society of America, PM4D–2 (2017)

Horst, F., Green, W.M., Assefa, S., Shank, S.M., Vlasov, Y.A., Offrein, B.J.: Cascaded Mach-Zehnder wavelength filters in silicon photonics for low loss and flat pass-band WDM (de-)multiplexing. Opt. Express 21(10), 11652–11658 (2013)

doi: 10.1364/OE.21.011652

Zhuang, L., Zhu, C., Xie, Y., Burla, M., Roeloffzen, C.G.H., Hoekman, M., Corcoran, B., Lowery, A.J.: Nyquist-filtering (de) multiplexer using ring resonator assisted interferometer circuit. J. Lightwave Technol. 34(8), 1732–1738 (2016)

doi: 10.1109/JLT.2015.2502251

Rivai, M., Sardjono, T.A., Purwanto, D.: Investigation of michelson interferometer for volatile organic compound sensor. J. Phys. Conf. Ser. 853, 012017 (2017)

doi: 10.1088/1742-6596/853/1/012017

Shiokawa, K., Otsuka, Y., Oyama, S., Nozawa, S., Satoh, M., Katoh, Y., Hamaguchi, Y., Yamamoto, Y., Meriwether, J.: Development of low-cost sky-scanning Fabry-Perot interferometers for airglow and auroral studies. Earth Planet Space 64, 1033–1046 (2012)

doi: 10.5047/eps.2012.05.004

Zhang, P., Tang, M., Gao, F., Zhu, B., Zhao, Z., Duan, L., Fu, S., Ouyang, J., Wei, H., Shum, P.P. Liu, D.: Simplified hollow-core fiber-based fabry-perot interferometer with modified vernier effect for highly sensitive high-temperature measurement. IEEE Photon. J. 7, 1–10 (2017)

Wang, C., Sun, J., Yang, C., Kuang, B., Fang, D., Asundi, A.: Research on a novel Fabry-Perot interferometer model based on the ultra-small gradient-index fiber probe. Sensors 19, 1538 (2019)

doi: 10.3390/s19071538

Kuhn, J., Bobrowski, N., Boudoire, G., Calabrese, S., Giuffrida, G., Liuzzo, M., Karume, K., Tedesco, D., Wagner, T., Platt, U.: High-spectral-resolution Fabry-Pérot interferometers overcome fundamental limitations of present volcanic gas remote sensing techniques. Front. Earth Sci. 11, 1039093 (2023)

doi: 10.3389/feart.2023.1039093

Karimeddiny, S., Cham, T.M.J., Smedley, O., Ralph, D.C., Luo, Y.K.: Sagnac interferometry for high-sensitivity optical measurements of spin-orbit torque. Sci. Adv. 9, eadi9039 (2023)

doi: 10.1126/sciadv.adi9039

Schubert, C., Abend, S., Gersemann, M., Gebbe, M., Schlippert, D., Berg, P., Rasel, E.M.: Multi-loop atomic Sagnac interferometry. Sci. Rep. 11, 16121 (2021)

doi: 10.1038/s41598-021-95334-7

Barrett, B., Geiger, R., Dutta, I., Meunier, M., Canuel, B., Gauguet, A., Bouyer, P., Landragin, A.: The Sagnac effect: 20 years of development in matter-wave interferometry. Comptes Rendus Physique 15(10), 875–883 (2014)

doi: 10.1016/j.crhy.2014.10.009

Vakhtin, A.B., Kane, D.J., Wood, W.R., Peterson, K.A.: Common-path interferometer for frequency-domain optical coherence tomography. Appl. Opt. 42, 6953–6958 (2003)

doi: 10.1364/AO.42.006953

Barth, I., Conteduca, D., Reardon, C., Johnson, S., Krauss, T.F.: Common-path interferometric label-free protein sensing with resonant dielectric nanostructures. Light Sci. Appl. 9, 96 (2020)

doi: 10.1038/s41377-020-0336-6

Rao, Y.J., Jackson, D.A.: Principles of fiber-optic interferometry. In: Grattan, K.T.V., Meggitt, B.T. (eds.) Optical fiber sensor technology. Springer, Boston (2000)

Li, L., Xia, L., Xie, Z., Liu, D.: All-fiber Mach-Zehnder interferometers for sensing applications. Opt. Express 20, 11109–11120 (2012)

doi: 10.1364/OE.20.011109

Rozema, L.A., Wang, C., Mahler, D.H., Hayat, A., Steinberg, A.M., Sipe, J.E., Liscidini, M.: Characterizing an entangled-photon source with classical detectors and measurements. Optica 2, 430–433 (2015)

doi: 10.1364/OPTICA.2.000430

Li, Y.: Methods of generating entangled photon pairs. J. Phys. Conf. Ser. 1634, 012172 (2020)

doi: 10.1088/1742-6596/1634/1/012172

Ruihong, Q., Ying, M.: Research progress of quantum repeaters. J. Phys. Conf. Ser. 1237, 052032 (2019)

doi: 10.1088/1742-6596/1237/5/052032

Kamin, L., Shchukin, E., Schmidt, F., van Loock, P.: Exact rate analysis for quantum repeaters with imperfect memories and entanglement swapping as soon as possible. Phys. Rev. Res. 5, 023086 (2023)

doi: 10.1103/PhysRevResearch.5.023086

Palima, D., Bañas, A.R., Vizsnyiczai, G., Kelemen, L., Ormos, P., Glückstad, J.: Wave-guided optical waveguides. Opt. Express 20(3), 2004–2014 (2012)

doi: 10.1364/OE.20.002004

Wu, L.: Ultrathin waveguides for 2D photonic integrated circuits. Nat. Rev. Phys. 5, 634 (2023)

doi: 10.1038/s42254-023-00657-1

Lee, M., Hong, H., Yu, J., Mujid, F., Ye, A., Liang, C., Park, J.: Wafer-scale δ waveguides for integrated two-dimensional photonics. Science 381, 648–653 (2023)

doi: 10.1126/science.adi2322

Lvovsky, A.I.: Squeezed light, photonics: scientific foundations. Technol. Appl. 1, 121 (2015)

Tse, M., Yu, H., Kijbunchoo, N., Fernandez-Galiana, A., Dupej, P., Barsotti, L., Blair, C.D., Brown, D.D., Dwyer, S.E., Effler, A., Evans, M., Fritschel, P., Frolov, V.V., Green, A.C., Mansell, G.L., Matichard, F., Mavalvala, N., McClelland, D.E., McCuller, L., McRae, T., Miller, J., Mullavey, A., Oelker, E., Phinney, I.Y., Sigg, D., Slagmolen, B.J.J., Vo, T., Ward, R.L., Whittle, C., Abbott, R., Adams, C., Adhikari, R.X., Ananyeva, A., Appert, S., Arai, K., Areeda, J.S., Asali, Y., Aston, S.M., Austin, C., Baer, A.M., Ball, M., Ballmer, S.W., Banagiri, S., Barker, D., Bartlett, J., Berger, B.K., Betzwieser, J., Bhattacharjee, D., Billingsley, G., Biscans, S., Blair, R.M., Bode, N., Booker, P., Bork, R., Bramley, A., Brooks, A.F., Buikema, A., Cahillane, C., Cannon, K.C., Chen, X., Ciobanu, A.A., Clara, F., Cooper, S.J., Corley, K.R., Countryman, S.T., Covas, P.B., Coyne, D.C., Datrier, L.E.H., Davis, D., Di Fronzo, C., Driggers, J.C., Etzel, T., Evans, T.M., Feicht, J., Fulda, P., Fyffe, M., Giaime, J.A., Giardina, K.D., Godwin, P., Goetz, E., Gras, S., Gray, C., Gray, R., Gupta, A., Gustafson, E.K., Gustafson, R., Hanks, J., Hanson, J., Hardwick, T., Hasskew, R.K., Heintze, M.C., Helmling-Cornell, A.F., Holland, N.A., Jones, J.D., Kandhasamy, S., Karki, S., Kasprzack, M., Kawabe, K., King, P.J., Kissel, J.S., Kumar, R., Landry, M., Lane, B.B., Lantz, B., Laxen, M., Lecoeuche, Y.K., Leviton, J., Liu, J., Lormand, M., Lundgren, A.P., Macas, R., MacInnis, M., Macleod, D.M., Márka, S., Márka, Z., Martynov, D.V., Mason, K., Massinger, T.J., McCarthy, R., McCormick, S., McIver, J., Mendell, G., Merfeld, K., Merilh, E.L., Meylahn, F., Mistry, T., Mittleman, R., Moreno, G., Mow-Lowry, C.M., Mozzon, S., Nelson, T.J.N., Nguyen, P., Nuttall, L.K., Oberling, J., Oram, R.J., O’Reilly, B., Osthelder, C., Ottaway, D.J., Overmier, H., Palamos, J.R., Parker, W., Payne, E., Pele, A., Perez, C.J., Pirello, M., Radkins, H., Ramirez, K.E., Richardson, J.W., Riles, K., Robertson, N.A., Rollins, J.G., Romel, C.L., Romie, J.H., Ross, M.P., Ryan, K., Sadecki, T., Sanchez, E.J., Sanchez, L.E., Saravanan, T.R., Savage, R.L., Schaetzl, D., Schnabel, R., Schofield, R.M.S., Schwartz, E., Sellers, D., Shaffer, T.J., Smith, J.R., Soni, S., Sorazu, B., Spencer, A.P., Strain, K.A., Sun, L., Szczepańczyk, M.J., Thomas, M., Thomas, P., Thorne, K.A., Toland, K., Torrie, C.I., Traylor, G., Urban, A.L., Vajente, G., Valdes, G., Vander-Hyde, D.C., Veitch, P.J., Venkateswara, K., Venugopalan, G., Viets, A.D., Vorvick, C., Wade, M., Warner, J., Weaver, B., Weiss, R., Willke, B., Wipf, C.C., Xiao, L., Yamamoto, H., Yap, M.J., Yu, H., Zhang, L., Zucker, M.E., Zweizig, J.: Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019)

Huh, J., Guerreschi, G.G., Peropadre, B., McClean, J.R., Aspuru-Guzik, A.: Boson sampling for molecular vibronic spectra. Nat. Photon. 9, 615 (2015)

doi: 10.1038/nphoton.2015.153

Arrazola, J.M., Bromley, T.R.: Using Gaussian boson sampling to find dense subgraphs. Phys. Rev. Lett. 121, 030503 (2018)

doi: 10.1103/PhysRevLett.121.030503

Otterpohl, A., Sedlmeir, F., Vogl, U., Dirmeier, T., Shafiee, G., Schunk, G., Strekalov, D.V., Schwefel, H.G.L., Gehring, T., Andersen, U.L., Leuchs, G., Marquardt, C.: Squeezed vacuum states from a whispering gallery mode resonator. Optica 6, 1375 (2019)

doi: 10.1364/OPTICA.6.001375

Anderson, M.E., Beck, M., Raymer, M., Bierlein, J.: Quadrature squeezing with ultrashort pulses in nonlinear-optical waveguides. Opt. Lett. 20, 620 (1995)

doi: 10.1364/OL.20.000620

Mondain, F., Lunghi, T., Zavatta, A., Gouzien, E., Doutre, F., De Micheli, M., Tanzilli, S., D’Auria, V.: Chip-based squeezing at a telecom wavelength. Photon. Res. 7, A36 (2019)

doi: 10.1364/PRJ.7.000A36

Dutt, A., Luke, K., Manipatruni, S., Gaeta, A.L., Nussenzveig, P., Lipson, M.: On-chip optical squeezing. Phys. Rev. Appl. 3, 044005 (2015)

doi: 10.1103/PhysRevApplied.3.044005

Dutt, A., Miller, S., Luke, K., Cardenas, J., Gaeta, A.L., Nussenzveig, P., Lipson, M.: Tunable squeezing using coupled ring resonators on a silicon nitride chip. Opt. Lett. 41, 223 (2016)

doi: 10.1364/OL.41.000223

Vaidya, V.D., Morrison, B., Helt, L.G., Shahrokshahi, R., Mahler, D.H., Collins, M.J., Tan, K., Lavoie, J., Repingon, A., Menotti, M., Quesada, N., Pooser, R.C., Lita, A.E., Gerrits, T., Nam, S.W., Vernon, Z.: Broadband quadrature-squeezed vacuum and nonclassical photon number correlations from a nanophotonic device. Sci. Adv. 6, eaba9186 (2020)

doi: 10.1126/sciadv.aba9186

Safavi-Naeini, A.H., Gröblacher, S., Hill, J.T., Chan, J., Aspelmeyer, M., Painter, O.: Squeezed light from a silicon micromechanical resonator. Nature 500, 185 (2013)

doi: 10.1038/nature12307

Cernansky, R., Politi, A.: Nanophotonic source of quadrature squeezing via self-phase modulation. APL Photon. 5, 101303 (2020)

doi: 10.1063/5.0024341

Huang, G., Lucas, E., Liu, J., Raja, A.S., Lihachev, G., Gorodetsky, M.L., Engelsen, N.J., Kippenberg, T.J.: Thermorefractive noise in silicon-nitride microresonators. Phys. Rev. A 99, 061801 (2019)

doi: 10.1103/PhysRevA.99.061801

Guo, Y., Zhang, W., Dong, S., Huang, Y., Peng, J.: Telecom-band degenerate-frequency photon pair generation in silicon microring cavities. Opt. Lett. 39, 2526 (2014)

doi: 10.1364/OL.39.002526

Vernon, Z., Quesada, N., Liscidini, M., Morrison, B., Menotti, M., Tan, K., Sipe, J.E.: Scalable squeezed-light source for continuous-variable quantum sampling. Phys. Rev. Appl. 12, 064024 (2019)

doi: 10.1103/PhysRevApplied.12.064024

Ast, S., Mehmet, M., Schnabel, R.: High-bandwidth squeezed light at 1550 nm from a compact monolithic ppktp cavity. Opt. Express 21, 13572 (2013)

doi: 10.1364/OE.21.013572

Helt, L.G., Brańczyk, A.M., Liscidini, M., Steel, M.J.: Parasitic photon-pair suppression via photonic stop-band engineering. Phys. Rev. Lett. 118, 073603 (2017)

doi: 10.1103/PhysRevLett.118.073603

Azzini, S., Grassani, D., Strain, M.J., Sorel, M., Helt, L.G., Sipe, J.E., Liscidini, M., Galli, M., Bajoni, D.: Ultra-low power generation of twin photons in a compact silicon ring resonator. Opt. Express 20, 23100 (2012)

doi: 10.1364/OE.20.023100

Agha, I., Davanço, M., Thurston, B., Srinivasan, K.: Low-noise chip-based frequency conversion by four-wave-mixing bragg scattering in SiN

doi: 10.1364/OL.37.002997

Zhao, Y., Okawachi, Y., Jang, J.K., Ji, X., Lipson, M., Gaeta, A.L.: Near-degenerate quadrature-squeezed vacuum generation on a silicon-nitride chip. Phys. Rev. Lett. 124, 193601 (2020)

doi: 10.1103/PhysRevLett.124.193601

Caves, C.M.: Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981)

doi: 10.1103/PhysRevD.23.1693

Caves, C.M.: Quantum-mechanical radiation-pressure fluctuations in an interferometer. Phys. Rev. Lett. 45, 75–79 (1980)

doi: 10.1103/PhysRevLett.45.75

Gerry, C., Knight, P., Knight, P.L.: Introductory Quantum Optics. Cambridge University Press (2005)

Kimble, H.J., Levin, Y., Matsko, A.B., Thorne, K.S., Vyatchanin, S.P.: Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics. Phys. Rev. D 65, 022002 (2001)

doi: 10.1103/PhysRevD.65.022002

Aasi, J., Abadie, J., Abbott, B., Abbott, R., Abbott, T.D., Abernathy, M.R., Adams, C., Adams, T., Addesso, P., Adhikari, R.X., Affeldt, C., Aguiar, O.D., Ajith, P., Allen, B., Amador Ceron, E., Amariutei, D., Anderson, S.B., Anderson, W.G., Arai, K., Araya, M.C., Arceneaux, C., Ast, S., Aston, S.M., Atkinson, D., Aufmuth, P., Aulbert, C., Austin, L., Aylott, B.E., Babak, S., Baker, P.T., Ballmer, S., Bao, Y., Barayoga, J.C., Barker, D., Barr, B., Barsotti, L., Barton, M.A., Bartos, I., Bassiri, R., Batch, J., Bauchrowitz, J., Behnke, B., Bell, A.S., Bell, C., Bergmann, G., Berliner, J.M., Bertolini, A., Betzwieser, J., Beveridge, N., Beyersdorf, P.T., Bhadbhade, T., Bilenko, I.A., Billingsley, G., Birch, J., Biscans, S., Black, E., Blackburn, J.K., Blackburn, L., Blair, D., Bland, B., Bock, O., Bodiya, T.P., Bogan, C., Bond, C., Bork, R., Born, M., Bose, S., Bowers, J., Brady, P.R., Braginsky, V.B., Brau, J.E., Breyer, J., Bridges, D.O., Brinkmann, M., Britzger, M., Brooks, A.F., Brown, D.A., Brown, D.D., Buckland, K., Brückner, F., Buchler, B.C., Buonanno, A., Burguet-Castell, J., Byer, R.L., Cadonati, L., Camp, J.B., Campsie, P., Cannon, K., Cao, J., Capano, C.D., Carbone, L., Caride, S., Castiglia, A.D., Caudill, S., Cavaglià, M., Cepeda, C., Chalermsongsak, T., Chao, S., Charlton, P., Chen, X., Chen, Y., Cho, H.S., Chow, J.H., Christensen, N., Chu, Q., Chua, S.S.Y., Chung, C.T.Y., Ciani, G., Clara, F., Clark, D.E., Clark, J.A., Constancio Junior, M., Cook, D., Corbitt, T.R., Cordier, M., Cornish, N., Corsi, A., Costa, C.A., Coughlin, M.W., Countryman, S., Couvares, P., Coward, D.M., Cowart, M., Coyne, D.C., Craig, K., Creighton, J.D.E., Creighton, T.D., Cumming, A., Cunningham, L., Dahl, K., Damjanic, M., Danilishin, S.L., Danzmann, K., Daudert, B., Daveloza, H., Davies, G.S., Daw, E.J., Dayanga, T., Deleeuw, E., Denker, T., Dent, T., Dergachev, V., DeRosa, R., DeSalvo, R., Dhurandhar, S., Di Palma, I., Díaz, M., Dietz, A., Donovan, F., Dooley, K.L., Doravari, S., Drasco, S., Drever, R.W.P., Driggers, J.C., Du, Z., Dumas, J.C., Dwyer, S., Eberle, T., Edwards, M., Effler, A., Ehrens, P., Eikenberry, S.S., Engel, R., Essick, R., Etzel, T., Evans, K., Evans, M., Evans, T., Factourovich, M., Fairhurst, S., Fang, Q., Farr, B.F., Farr, W., Favata, M., Fazi, D., Fehrmann, H., Feldbaum, D., Finn, L.S., Fisher, R.P., Foley, S., Forsi, E., Fotopoulos, N., Frede, M., Frei, M.A., Frei, Z., Freise, A., Frey, R., Fricke, T.T., Friedrich, D., Fritschel, P., Frolov, V.V., Fujimoto, M.K., Fulda, P.J., Fyffe, M., Gair, J., Garcia, J., Gehrels, N., Gelencser, G., Gergely, L.Á., Ghosh, S., Giaime, J.A., Giampanis, S., Giardina, K.D., Gil-Casanova, S., Gill, C., Gleason, J., Goetz, E., González, G., Gordon, N., Gorodetsky, M.L., Gossan, S., Goßler, S., Graef, C., Graff, P.B., Grant, A., Gras, S., Gray, C., Greenhalgh, R.J.S., Gretarsson, A.M., Griffo, C., Grote, H., Grover, K., Grunewald, S., Guido, C., Gustafson, E.K., Gustafson, R., Hammer, D., Hammond, G., Hanks, J., Hanna, C., Hanson, J., Haris, K., Harms, J., Harry, G.M., Harry, I.W., Harstad, E.D., Hartman, M.T., Haughian, K., Hayama, K., Heefner, J., Heintze, M.C., Hendry, M.A., Heng, I.S., Heptonstall, A.W., Heurs, M., Hewitson, M., Hild, S., Hoak, D., Hodge, K.A., Holt, K., Holtrop, M., Hong, T., Hooper, S., Hough, J., Howell, E.J., Huang, V., Huerta, E.A., Hughey, B., Huttner, S.H., Huynh, M., Huynh-Dinh, T., Ingram, D.R., Inta, R., Isogai, T., Ivanov, A., Iyer, B.R., Izumi, K., Jacobson, M., James, E., Jang, H., Jang, Y.J., Jesse, E., Johnson, W.W., Jones, D., Jones, D.I., Jones, R., Ju, L., Kalmus, P., Kalogera, V., Kandhasamy, S., Kang, G., Kanner, J.B., Kasturi, R., Katsavounidis, E., Katzman, W., Kaufer, H., Kawabe, K., Kawamura, S., Kawazoe, F., Keitel, D., Kelley, D.B., Kells, W., Keppel, D.G., Khalaidovski, A., Khalili, F.Y., Khazanov, E.A., Kim, B.K., Kim, C., Kim, K., Kim, N., Kim, Y.M., King, P.J., Kinzel, D.L., Kissel, J.S., Klimenko, S., Kline, J., Kokeyama, K., Kondrashov, V., Koranda, S., Korth, W.Z., Kozak, D., Kozameh, C., Kremin, A., Kringel, V., Krishnan, B., Kucharczyk, C., Kuehn, G., Kumar, P., Kumar, R., Kuper, B.J., Kurdyumov, R., Kwee, P., Lam, P.K., Landry, M., Lantz, B., Lasky, P.D., Lawrie, C., Lazzarini, A., Le Roux, A., Leaci, P., Lee, C.H., Lee, H.K., Lee, H.M., Lee, J., Leong, J.R., Levine, B., Lhuillier, V., Lin, A.C., Litvine, V., Liu, Y., Liu, Z., Lockerbie, N.A., Lodhia, D., Loew, K., Logue, J., Lombardi, A.L., Lormand, M., Lough, J., Lubinski, M., Lück, H., Lundgren, A.P., Macarthur, J., Macdonald, E., Machenschalk, B., MacInnis, M., Macleod, D.M., Magaña-Sandoval, F., Mageswaran, M., Mailand, K., Manca, G., Mandel, I., Mandic, V., Márka, S., Márka, Z., Markosyan, A.S., Maros, E., Martin, I.W., Martin, R.M., Martinov, D., Marx, J.N., Mason, K., Matichard, F., Matone, L., Matzner, R.A., Mavalvala, N., May, G., Mazzolo, G., McAuley, K., McCarthy, R., McClelland, D.E., McGuire, S.C., McIntyre, G., McIver, J., Meadors, G.D., Mehmet, M., Meier, T., Melatos, A., Mendell, G., Mercer, R.A., Meshkov, S., Messenger, C., Meyer, M.S., Miao, H., Miller, J., Mingarelli, C.M.F., Mitra, S., Mitrofanov, V.P., Mitselmakher, G., Mittleman, R., Moe, B., Mokler, F., Mohapatra, S.R.P., Moraru, D., Moreno, G., Mori, T., Morriss, S.R., Mossavi, K., Mow-Lowry, C.M., Mueller, C.L., Mueller, G., Mukherjee, S., Mullavey, A., Munch, J., Murphy, D., Murray, P.G., Mytidis, A., Nanda Kumar, D., Nash, T., Nayak, R., Necula, V., Newton, G., Nguyen, T., Nishida, E., Nishizawa, A., Nitz, A., Nolting, D., Normandin, M.E., Nuttall, L.K., O’Dell, J., O’Reilly, B., O’Shaughnessy, R., Ochsner, E., Oelker, E., Ogin, G.H., Oh, J.J., Oh, S.H., Ohme, F., Oppermann, P., Osthelder, C., Ott, C.D., Ottaway, D.J., Ottens, R.S., Ou, J., Overmier, H., Owen, B.J., Padilla, C., Pai, A., Pan, Y., Pankow, C., Papa, M.A., Paris, H., Parkinson, W., Pedraza, M., Penn, S., Peralta, C., Perreca, A., Phelps, M., Pickenpack, M., Pierro, V., Pinto, I.M., Pitkin, M., Pletsch, H.J., Pöld, J., Postiglione, F., Poux, C., Predoi, V., Prestegard, T., Price, L.R., Prijatelj, M., Privitera, S., Prokhorov, L.G., Puncken, O., Quetschke, V., Quintero, E., Quitzow-James, R., Raab, F.J., Radkins, H., Raffai, P., Raja, S., Rakhmanov, M., Ramet, C., Raymond, V., Reed, C.M., Reed, T., Reid, S., Reitze, D.H., Riesen, R., Riles, K., Roberts, M., Robertson, N.A., Robinson, E.L., Roddy, S., Rodriguez, C., Rodriguez, L., Rodruck, M., Rollins, J.G., Romie, J.H., Röver, C., Rowan, S., Rüdiger, A., Ryan, K., Salemi, F., Sammut, L., Sandberg, V., Sanders, J., Sankar, S., Sannibale, V., Santamaría, L., Santiago-Prieto, I., Santostasi, G., Sathyaprakash, B.S., Saulson, P.R., Savage, R.L., Schilling, R., Schnabel, R., Schofield, R.M.S., Schuette, D., Schulz, B., Schutz, B.F., Schwinberg, P., Scott, J., Scott, S.M., Seifert, F., Sellers, D., Sengupta, A.S., Sergeev, A., Shaddock, D.A., Shahriar, M.S., Shaltev, M., Shao, Z., Shapiro, B., Shawhan, P., Shoemaker, D.H., Sidery, T.L., Siemens, X., Sigg, D., Simakov, D., Singer, A., Singer, L., Sintes, A.M., Skelton, G.R., Slagmolen, B.J.J., Slutsky, J., Smith, J.R., Smith, M.R., Smith, R.J.E., Smith-Lefebvre, N.D., Son, E.J., Sorazu, B., Souradeep, T., Stefszky, M., Steinert, E., Steinlechner, J., Steinlechner, S., Steplewski, S., Stevens, D., Stochino, A., Stone, R., Strain, K.A., Strigin, S.E., Stroeer, A.S., Stuver, A.L., Summerscales, T.Z., Susmithan, S., Sutton, P.J., Szeifert, G., Talukder, D., Tanner, D.B., Tarabrin, S.P., Taylor, R., Thomas, M., Thomas, P., Thorne, K.A., Thorne, K.S., Thrane, E., Tiwari, V., Tokmakov, K.V., Tomlinson, C., Torres, C.V., Torrie, C.I., Traylor, G., Tse, M., Ugolini, D., Unnikrishnan, C.S., Vahlbruch, H., Vallisneri, M., van der Sluys, M.V., van Veggel, A.A., Vass, S., Vaulin, R., Vecchio, A., Veitch, P.J., Veitch, J., Venkateswara, K., Verma, S., Vincent-Finley, R., Vitale, S., Vo, T., Vorvick, C., Vousden, W.D., Vyatchanin, S.P., Wade, A., Wade, L., Wade, M., Waldman, S.J., Wallace, L., Wan, Y., Wang, M., Wang, J., Wang, X., Wanner, A., Ward, R.L., Was, M., Weinert, M., Weinstein, A.J., Weiss, R., Welborn, T., Wen, L., Wessels, P., West, M., Westphal, T., Wette, K., Whelan, J.T., Whitcomb, S.E., Wiseman, A.G., White, D.J., Whiting, B.F., Wiesner, K., Wilkinson, C., Willems, P.A., Williams, L., Williams, R., Williams, T., Willis, J.L., Willke, B., Wimmer, M., Winkelmann, L., Winkler, W., C. Wipf, C., Wittel, H., Woan, G., Wooley, R., Worden, J., Yablon, J., Yakushin, I., Yamamoto, H., Yancey, C.C., Yang, H., Yeaton-Massey, D., Yoshida, S., Yum, H., Zanolin, M., Zhang, F., Zhang, L., Zhao, C., Zhu, H., Zhu, X.J., Zotov, N., Zucker, M.E., Zweizig, J.: Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013)

Grote, H., Danzmann, K., Dooley, K.L., Schnabel, R., Slutsky, J., Vahlbruch, H.: First long-term application of squeezed states of light in a gravitational-wave observatory. Phys. Rev. Lett. 110, 181101 (2013)

doi: 10.1103/PhysRevLett.110.181101

The LIGO Scientific Collaboration. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7, 962 (2011)

doi: 10.1038/nphys2083

Backes, K.M., Palken, D.A., Kenany, S.A., Brubaker, B.M., Cahn, S.B., Droster, A., Hilton, G.C., Ghosh, S., Jackson, H., Lamoreaux, S.K., Leder, A.F., Lehnert, K.W., Lewis, S.M., Malnou, M., Maruyama, R.H., Rapidis, N.M., Simanovskaia, M., Singh, S., Speller, D.H., Urdinaran, I., Vale, L.R., van Assendelft, E.C., van Bibber, K., Wang, H.: A quantum enhanced search for dark matter axions. Nature 590, 238–242 (2021)

Aggarwal, N., Cullen, T.J., Cripe, J., Cole, G.D., Lanza, R., Libson, A., Follman, D., Heu, P., Corbitt, T., Mavalvala, N.: Room-temperature optomechanical squeezing. Nat. Phys. 16, 784–788 (2020)

doi: 10.1038/s41567-020-0877-x

Qiu, J.Y., Grimsmo, A., Peng, K., Kannan, B., Lienhard, B., Sung, Y., Krantz, P., Bolkhovsky, V., Calusine, G., Kim, D., Melville, A., Niedzielski, B., Yoder, J., Schwartz, M., Orlando, T., Siddiqi, I., Gustavsson, S., O’Brien, K., Oliver, W.: Broadband squeezed microwaves and amplification with a Josephson travelling-wave parametric amplifier. Nat. Phys. 19, 706–713 (2023)

Murch, K., Weber, S., Beck, K., Ginossar, E., Siddiqi, I.: Reduction of the radiative decay of atomic coherence in squeezed vacuum. Nature 499, 62–65 (2013)

doi: 10.1038/nature12264

Eichler, C., Salathe, Y., Mlynek, J., Schmidt, S., Wallraff, A.: Quantum-limited amplification and entanglement in coupled nonlinear resonators. Phys. Rev. Lett. 113, 110502 (2014)

doi: 10.1103/PhysRevLett.113.110502

Brooks, D.W.C., Botter, T., Schreppler, S., Purdy, T.P., Brahms, N., Stamper-Kurn, D.M.: Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476–480 (2012)

doi: 10.1038/nature11325

Purdy, T.P., Yu, P.L.L., Peterson, R.W., Kampel, N.S., Regal, C.A.: Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013)

Sudhir, V., Wilson, D.J., Schilling, R., Schütz, H., Fedorov, S.A., Ghadimi, A.H., Nunnenkamp, A., Kippenberg, T.J.: Appearance and disappearance of quantum correlations in measurement-based feedback control of a mechanical oscillator. Phys. Rev. X 7, 011001 (2017)

Ockeloen-Korppi, C.F., Damskägg, E., Paraoanu, G.S., Massel, F., Sillanpää, M.A.: Revealing hidden quantum correlations in an electromechanical measurement. Phys. Rev. Lett. 121, 243601 (2018)

doi: 10.1103/PhysRevLett.121.243601

Barzanjeh, S., Redchenko, E.S., Peruzzo, M., Wulf, M., Lewis, D.P., Arnold, G., Fink, J.M.: Stationary entangled radiation from micromechanical motion. Nature 570, 480–483 (2019)

doi: 10.1038/s41586-019-1320-2

Andersen, U.L., Gehring, T., Marquardt, C., Leuchs, G.: 30 years of squeezed light generation. Phys. Scr. 91, 053001 (2016)

doi: 10.1088/0031-8949/91/5/053001

Arnbak, J., Jacobsen, C.S., Andrade, R.B., Guo, X., Neergaard-Nielsen, J.S., Andersen, U.L., Gehring, T.: Compact, low-threshold squeezed light source. Opt. Express 27, 37877–37885 (2019)

doi: 10.1364/OE.27.037877

McCuller, L., Whittle, C., Ganapathy, D., Komori, K., Tse, M., Fernandez-Galiana, A., Barsotti, L., Fritschel, P., MacInnis, M., Matichard, F., Mason, K., Mavalvala, N., Mittleman, R., Yu, H., Zucker, M.E., Evans, M.: Frequency-dependent squeezing for advanced LIGO. Phys. Rev. Lett. 124, 171102 (2020)

doi: 10.1103/PhysRevLett.124.171102

Darsow-Fromm, C., Gurs, J., Schnabel, R., Steinlechner, S.: Squeezed light at 2128 nm for future gravitational-wave observatories. Opt. Lett. 46, 5850 (2021)

doi: 10.1364/OL.433878

Schnabel, R., Schönbeck, A.: The Squeeze Laser. IEEE Trans. Quantum Eng.: Quantum Sens. Metrol. 3, 3500209 (2022)

doi: 10.1109/TQE.2022.3224686

Abdo, B.: Broadband squeezer of microwave light. Nat. Phys. 19, 616–617 (2023)

Miller, J.L.: Frequency-dependent squeezing makes LIGO even more sensitive. Phys. Today 77(1), 13–16 (2024)

doi: 10.1063/PT.3.5374

Young, S.M., Soh, D.: Fundamental limits to the generation of highly displaced bright squeezed light using linear optics and parametric amplifiers. arXive preprints arXiv:2311.08641 [quant-ph] (2023)

Aaronson, S., Arkhipov, A.: The computational complexity of linear optics. In: Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing. pp. 333–342 (2011)

Barrett, J., Hardy, L., Kent, A.: No signaling and quantum key distribution. Phys. Rev. Lett. 95, 010503 (2005)

doi: 10.1103/PhysRevLett.95.010503

Raussendorf, R., Harrington, J.: Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007)

doi: 10.1103/PhysRevLett.98.190504

Andrini, G., Amanti, F., Armani, F., Bellani, V., Bonaiuto, V., Cammarata, S., Campostrini, M., Dao, T.H., De Matteis, F., Demontis, V., Di Giuseppe, G., Ditalia Tchernij, S., Donati, S., Fontana, A., Forneris, J., Francini, R., Frontini, L., Gunnella, R., Iadanza, S., Kaplan, A.E., Lacava, C., Liberali, V., Marzioni, F., Nieto Hernández, E., Pedreschi, E., Piergentili, P., Prete, D., Prosposito, P., Rigato, V., Roncolato, C., Rossella, F., Salamon, A., Salvato, M., Sargeni, F., Shojaii, J., Spinella, F., Stabile, A., Toncelli, A., Trucco, G., Vitali, V.: Solid-state color centers for single-photon generation. Photonics 11(2), 188 (2024)

Wei, Y., Liu, S., Li, X., Yu, Y., Su, X., Li, S., Shang, X., Liu, H., Hao, H., Ni, H., Yu, S., Niu, Z., Iles-Smith, J., Liu, J., Wang, X.: Tailoring solid-state single-photon sources with stimulated emissions. Nat. Nanotechnol. 17, 470–476 (2022)

doi: 10.1038/s41565-022-01092-6

Zhu, C., Marczak, M., Feld, L., Boehme, S.C., Bernasconi, C., Moskalenko, A., Cherniukh, I., Dirin, D., Bodnarchuk, M.I., Kovalenko, M.V., Rainò, G.: Room-temperature, highly pure single-photon sources from all-inorganic lead halide perovskite quantum dots. Nano Lett. 22(9), 3751–3760 (2022)

doi: 10.1021/acs.nanolett.2c00756

Hong, C.K., Ou, Z.Y., Mandel, L.: Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59(18), 2044 (1987)

doi: 10.1103/PhysRevLett.59.2044

Tomm, N., Javadi, A., Antoniadis, N.O., Najer, D., Löbl, M.C., Korsch, A.R., Schott, R., Valentin, S.R., Wieck, A.D., Ludwig, A., Warburton, R.J.: A bright and fast source of coherent single photons. Nat. Nanotechnol. 16, 399–403 (2021)

doi: 10.1038/s41565-020-00831-x

Ghosh, R., Mandel, L.: Observation of nonclassical effects in the interference of two photons. Phys. Rev. Lett. 59(17), 1903 (1987)

doi: 10.1103/PhysRevLett.59.1903

Kwiat, P.G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A.V., Shih, Y.: New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75(24), 4337 (1995)

doi: 10.1103/PhysRevLett.75.4337

Kaneda, F., Christensen, B.G., Wong, J.J., Park, H.S., McCusker, K.T., Kwiat, P.G.: Time-multiplexed heralded single-photon source. Optica 2(12), 1010 (2015)

doi: 10.1364/OPTICA.2.001010

Clauser, J.F.: Experimental distinction between the quantum and classical field theoretic predictions for the photoelectric effect. Phys. Rev. D 9(4), 853 (1974)

doi: 10.1103/PhysRevD.9.853

Diedrich, F., Walther, H.: Nonclassical radiation of a single stored ion. Phys. Rev. Lett. 58(3), 203 (1987)

doi: 10.1103/PhysRevLett.58.203

Kimble, H.J., Dagenais, M., Mandel, L.: Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39(11), 691 (1977)

doi: 10.1103/PhysRevLett.39.691

Moerner, W.E., Kador, L.: Optical detection and spectroscopy of single molecules in a solid. Phys. Rev. Lett. 62(21), 2535 (1989)

doi: 10.1103/PhysRevLett.62.2535

Kurtsiefer, C., Mayer, S., Zarda, P., Weinfurter, H.: Stable solid-state source of single photons. Phys. Rev. Lett. 85(2), 290 (2000)

doi: 10.1103/PhysRevLett.85.290

Michler, P., Kiraz, A., Becher, C., Schoenfeld, W.V., Petroff, P., Zhang, L., Hu, E.L., Imamoglu, A.: A quantum dot single-photon turnstile device. Science 290(5500), 2282 (2000)

doi: 10.1126/science.290.5500.2282

Castelletto, S., Johnson, B.C., Ivády, V., Stavrias, N., Umeda, T., Gali, A., Ohshima, T.: A silicon carbide room-temperature single-photon source. Nat. Mater. 13(2), 151 (2014)

doi: 10.1038/nmat3806

Tran, T.T., Bray, K., Ford, M.J., Toth, M., Aharonovich, I.: Quantum emission from hexagonal boron nitride monolayers. Nat. Nanotechnol. 11(1), 37 (2016)

doi: 10.1038/nnano.2015.242

Senellart, P., Solomon, G., White, A.: High-performance semiconductor quantum-dot single-photon sources. Nat. Nanotechnol. 12(11), 1026 (2017)

doi: 10.1038/nnano.2017.218

Wang, H., He, Y.M., Chung, T.H., Hu, H., Yu, Y., Chen, S., Ding, X., Chen, M.C., Qin, J., Yang, X., Liu, R.Z., Duan, Z.C., Li, J.P., Gerhardt, S., Winkler, K., Jurkat, J., Wang, L.J., Gregersen, N., Huo, Y.H., Dai, Q., Yu, S., Höfling, S., Lu, C.Y., Pan, J.W.: Towards optimal single-photon sources from polarized microcavities. Nat. Photon. 13(11), 770 (2019)

doi: 10.1038/s41566-019-0494-3

Varnava, M., Browne, D.E., Rudolph, T.: How good must single photon sources and detectors be for efficient linear optical quantum computation. Phys. Rev. Lett. 100(6), 060502 (2008)

doi: 10.1103/PhysRevLett.100.060502

Vahlbruch, H., Mehmet, M., Danzmann, K., Schnabel, R.: Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency. Phys. Rev. Lett. 117(11), 110801 (2016)

doi: 10.1103/PhysRevLett.117.110801

Furusawa, A., Sorensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S.: Unconditional quantum teleportation. Science 282(5389), 706 (1998)

doi: 10.1126/science.282.5389.706

Larsen, M.V., Guo, X., Breum, C.R., Neergaard-Nielsen, J.S., Andersen, U.L.: Deterministic generation of a two-dimensional cluster state. Science 366(6463), 369 (2019)

doi: 10.1126/science.aay4354

Tian, L., Li, S., Yuan, H., Wang, H.: Generation of narrow-band polarization-entangled photon pairs at a rubidium D1 line. J. Phys. Soc. Jpn. 85, 124403 (2016)

doi: 10.7566/JPSJ.85.124403

Jabir, M.V., Samanta, G.K.: Robust, high brightness, degenerate entangled photon source at room temperature. Sci. Rep. 7, 12613 (2017)

doi: 10.1038/s41598-017-12709-5

Weston, M.M., Chrzanowski, H.M., Wollmann, S., Boston, A., Ho, J., Shalm, L.K., Verma, V.B., Allman, M.S., Nam, S.W., Patel, R.B., Slussarenko, S.: Efficient and pure femtosecond-pulse-length source of polarization-entangled photons. Geoff. J. Opt. Express 24, 10869–10879 (2016)

doi: 10.1364/OE.24.010869

Kaneda, F., Garay-Palmett, K., U’Ren, A.B., Kwiat, P.G.: Heralded single-photon source utilizing highly nondegenerate, spectrally factorable spontaneous parametric downconversion. Opt. Express 24, 10733–10747 (2016)

doi: 10.1364/OE.24.010733

Vergyris, P., Meany, T., Lunghi, T., Sauder, G., Downes, J., Steel, M., Withford, M., Alibart, O., Tanzilli, S.: On-chip generation of heralded photon-number states. Sci. Rep. 6, 35975 (2016)

doi: 10.1038/srep35975

Krapick, S., Brecht, B., Herrmann, H., Quiring, V., Silberhorn, C.: On-chip generation of photon-triplet states. Opt. Express 24, 2836–2849 (2016)

doi: 10.1364/OE.24.002836

Montaut, N., Sansoni, L., Meyer-Scott, E., Ricken, R., Quiring, V., Herrmann, H., Silberhorn, C.: High-efficiency plug-and-play source of heralded single photons. Phys. Rev. Appl. 8, 024021 (2017)

doi: 10.1103/PhysRevApplied.8.024021

Vergyris, P., Kaiser, F., Gouzien, E., Sauder, G., Lunghi, T., Tanzilli, S.: Fully guided-wave photon pair source for quantum applications. Quantum Sci. Technol. 2, 024007 (2017)

doi: 10.1088/2058-9565/aa6ed2

Ding, D.S., Zhang, W., Shi, S., Zhou, Z.Y., Li, Y., Shi, B.S., Guo, G.C.: Hybrid-cascaded generation of tripartite telecom photons using an atomic ensemble and a nonlinear waveguide. Optica 2, 642–645 (2015)

doi: 10.1364/OPTICA.2.000642

Setzpfandt, F., Solntsev, A.S., Titchener, J., Wu, C.W., Xiong, C., Schiek, R., Pertsch, T., Neshev, D.N., Sukhorukov, A.A.: Tunable generation of entangled photons in a nonlinear directional coupler. Laser Photon. Rev. 10, 131–136 (2015)

doi: 10.1002/lpor.201500216

Guo, X., Zou, C.L., Schuck, C., Jung, H., Cheng, R., Tang, H.X.: Parametric down-conversion photon-pair source on a nanophotonic chip. Light Sci. Appl. 6, e16249 (2017)

doi: 10.1038/lsa.2016.249

Kultavewuti, P., Zhu, E.Y., Xing, X., Qian, L., Pusino, V., Sorel, M., Aitchison, J.S.: Polarization-entangled photon pair sources based on spontaneous four wave mixing assisted by polarization mode dispersion. Sci. Rep. 7, 5785 (2017)

doi: 10.1038/s41598-017-06010-8

Cruz-Delgado, D., Ramirez-Alarcon, R., Ortiz-Ricardo, E., Monroy-Ruz, J., Dominguez-Serna, F., Cruz-Ramirez, H., Garay-Palmett, K., U’Ren, A.B.: Fiber-based photon-pair source capable of hybrid entanglement in frequency and transverse mode, controllably scalable to higher dimensions. Sci. Rep. 6, 27377 (2016)

doi: 10.1038/srep27377

Rogers, S., Mulkey, D., Lu, X., Jiang, W.C., Lin, Q.: High visibility time-energy entangled photons from a silicon nanophotonic chip. ACS Photon. 3(10), 1754–1761 (2016)

doi: 10.1021/acsphotonics.6b00423

Cordier, M., Orieux, A., Gabet, R., Harlé, T., Dubreuil, N., Diamanti, E., Delaye, P., Zaquine, I.: Raman-tailored photonic crystal fiber for telecom band photon-pair generation. Opt. Lett. 42, 2583–2586 (2017)

doi: 10.1364/OL.42.002583

Yan, Z., Duan, Y., Helt, L.G., Ams, M., Withford, M.J., Steel, M.J.: Generation of heralded single photons beyond 1100 nm by spontaneous four-wave mixing in a side-stressed femtosecond laser-written waveguide. Appl. Phys. Lett. 107, 231106 (2015)

doi: 10.1063/1.4937374

Olbrich, F., Höschele, J., Müller, M., Kettler, J., Luca Portalupi, S., Paul, M., Jetter, M., Michler, P.: Polarization-entangled photons from an InGaAs-based quantum dot emitting in the telecom C-band. Appl. Phys. Lett. 111, 133106 (2017)

doi: 10.1063/1.4994145

Portalupi, S.L., Hornecker, G., Giesz, V., Grange, T., Lemaître, A., Demory, J., Sagnes, I., Lanzillotti-Kimura, N.D., Lanco, L., Auffèves, A., Senellart, P.: Bright phonon-tuned single-photon source. Nano Lett. 15(10), 6290–6294 (2015)

doi: 10.1021/acs.nanolett.5b00876

Somaschi, N., Giesz, V., De Santis, L., Loredo, J.C., Almeida, M.P., Hornecker, G., Portalupi, S.L., Grange, T., Antón, C., Demory, J., Gómez, C., Sagnes, I., Lanzillotti-Kimura, N.D., Lemaítre, A., Auffeves, A., White, A.G., Lanco, L., Senellart, P.: Near-optimal single-photon sources in the solid state. Nat. Photon 10, 340–345 (2016)

Loredo, J.C., Zakaria, N.A., Somaschi, N., Anton, C., De Santis, L., Giesz, V., Grange, T., Broome, M.A., Gazzano, O., Coppola, G., Sagnes, I.: Scalable performance in solid-state single-photon sources. Optica 3, 433–440 (2016)

doi: 10.1364/OPTICA.3.000433

Kiršanskė, G., Thyrrestrup, H., Daveau, R.S., Dreeßen, C.L., Pregnolato, T., Midolo, L., Tighineanu, P., Javadi, A., Stobbe, S., Schott, R., Ludwig, A., Wieck, A.D., Park, S.I., Song, J.D., Kuhlmann, A.V., Söllner, I., Löbl, M.C., Warburton, R.J., Lodahl, P.: Indistinguishable and efficient single photons from a quantum dot in a planar nanobeam waveguide. Phys. Rev. B 96, 165306 (2017)

Schlehahn, A., Fischbach, S., Schmidt, R., Kaganskiy, A., Strittmatter, A., Rodt, S., Heindel, T., Reitzenstein, S.: A stand-alone fiber-coupled single-photon source. Sci. Rep. 8, 1340 (2018)

doi: 10.1038/s41598-017-19049-4

Snijders, H., Frey, J.A., Norman, J., Post, V.P., Gossard, A.C., Bowers, J.E., van Exter, M.P., Löffler, W., Bouwmeester, D.: Fiber-coupled cavity-QED source of identical single photons. Phys. Rev. Appl. 9, 0310022018 (2018)

doi: 10.1103/PhysRevApplied.9.031002

Ding, X., He, Y., Duan, Z.C., Gregersen, N., Chen, M.C., Unsleber, S., Maier, S., Schneider, C., Kamp, M., Höfling, S., Lu, C.Y.: On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016)

doi: 10.1103/PhysRevLett.116.020401

Davanco, M., Liu, J., Sapienza, L., Zhang, C.Z., De Miranda Cardoso, J.V., Verma, V., Mirin, R., Nam, S.W., Liu, L., Srinivasan, K.: Heterogeneous integration for on-chip quantum photonic circuits with single quantum dot devices. Nat. Commun. 8, 889 (2017)

doi: 10.1038/s41467-017-00987-6

Heindel, T., Thoma, A., von Helversen, M., Schmidt, M., Schlehahn, A., Gschrey, M., Schnauber, P., Schulze, J.H., Strittmatter, A., Beyer, J., Rodt, S., Carmele, A., Knorr, A., Reitzenstein, S.: A bright triggered twin-photon source in the solid state. Nat. Commun. 8, 14870 (2017)

Huber, D., Reindl, M., Covre da Silva, S.F., Schimpf, C., Martín-Sánchez, J., Huang, H., Piredda, G., Edlinger, J., Rastelli, A., Trotta, R.: Strain-tunable GaAs quantum dot: a nearly dephasing-free source of entangled photon pairs on demand. Phys. Rev. Lett. 121, 033902 (2018)

Huber, D., Reindl, M., Huo, Y., Huang, H., Wildmann, J.S., Schmidt, O.G., Rastelli, A., Trotta, R.: Highly indistinguishable and strongly entangled photons from symmetric GaAs quantum dots. Nat. Commun. 8, 15506 (2017)

doi: 10.1038/ncomms15506

Jöns, K.D., Schweickert, L., Versteegh, M.A.M., Dalacu, D., Poole, P.J., Gulinatti, A., Giudice, A., Zwiller, V., Reimer, M.E.: Bright nanoscale source of deterministic entangled photon pairs violating Bell’s inequality. Sci. Rep. 7, 1700 (2017)

doi: 10.1038/s41598-017-01509-6

Khoshnegar, M., Huber, T., Predojević, A., Dalacu, D., Prilmüller, M., Lapointe, J., Wu, X., Tamarat, P., Lounis, B., Poole, P., Weihs, G., Majedi, H.: A solid state source of photon triplets based on quantum dot molecules. Nat. Commun. 8, 15716 (2017)

Benedikter, J., Kaupp, H., Hümmer, T., Liang, Y., Bommer, A., Becher, C., Krueger, A., Smith, J.M., Hänsch, T.W., Hunger, D.: Cavity-enhanced single-photon source based on the silicon-vacancy center in diamond. Phys. Rev. Appl. 7, 024031 (2017)

doi: 10.1103/PhysRevApplied.7.024031

Wang, X.L., Chen, L.K., Li, W., Huang, H.L., Liu, C., Chen, C., Luo, Y.H., Su, Z.E., Wu, D., Li, Z.D., Lu, H.: Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016)

doi: 10.1103/PhysRevLett.117.210502

Higginbottom, D.B., Slodička, L., Araneda, G., Lachman, L., Filip, R., Hennrich, M., Blatt, R.: Pure single photons from a trapped atom source. New J. Phys. 18, 093038 (2016)

doi: 10.1088/1367-2630/18/9/093038

Peng, Z., de Graaf, S., Tsai, J., Astafiev, O.V.: Tuneable on-demand single-photon source in the microwave range. Nat. Commun. 7, 12588 (2016)

doi: 10.1038/ncomms12588

Geng, W., Manceau, M., Rahbany, N., Sallet, V., De Vittorio, M., Carbone, L., Glorieux, Q., Bramati, A., Couteau, C.: Localised excitation of a single photon source by a nanowaveguide. Sci. Rep. 6, 19721 (2016)

doi: 10.1038/srep19721

Li, Y.H., Zhou, Z.Y., Feng, L.T., Fang, W.T., Liu, S.L., Liu, S.K., Wang, K., Ren, X.F., Ding, D.S., Xu, L.X., Shi, B.S.: On-chip multiplexed multiple entanglement sources in a single silicon nanowire. Phys. Rev. Appl. 7, 064005 (2017)

doi: 10.1103/PhysRevApplied.7.064005

Kruse, R., Sansoni, L., Brauner, S., Ricken, R., Hamilton, C.S., Jex, I., Silberhorn, C.: Dual-path source engineering in integrated quantum optics. Phys. Rev. A 92, 053841 (2015)

doi: 10.1103/PhysRevA.92.053841

Sansoni, L., Luo, K.H., Eigner, C., Ricken, R., Quiring, V., Herrmann, H., Silberhorn, C.: A two-channel, spectrally degenerate polarization entangled source on chip. npj Quantum Inf. 3, 5 (2017)

doi: 10.1038/s41534-016-0005-z

Atzeni, S., Rab, A.S., Corrielli, G., Polino, E., Valeri, M., Mataloni, P., Spagnolo, N., Crespi, A., Sciarrino, F., Osellame, R.: Integrated sources of entangled photons at the telecom wavelength in femtosecond-laser-written circuits. Optica 5, 311–314 (2018)

doi: 10.1364/OPTICA.5.000311

Lounis, B., Orrit, M.: Single-photon sources. Rep. Prog. Phys. 68, 1129 (2005)

doi: 10.1088/0034-4885/68/5/R04

Mäntynen, H., Anttu, N., Sun, Z., Lipsanen, H.: Single-photon sources with quantum dots in III-V nanowires. Nanophotonics 8(5), 747–769 (2019)

doi: 10.1515/nanoph-2019-0007

Sinha, U., Sahoo, S.N., Singh, A., Joarder, K., Chatterjee, R., Chakraborti, S.: Single-photon sources. Opt. Photon. News 30(9), 32–39 (2019)

doi: 10.1364/OPN.30.9.000032

Lee, J., Leong, V., Kalashnikov, D., Dai, J., Gandhi, A., Krivitsky, L.A.: Integrated single photon emitters. AVS Quantum Sci. 2, 031701 (2020)

doi: 10.1116/5.0011316

Ollivier, H., Maillette de Buy Wenniger, I., Thomas, S., Wein, S.C., Harouri, A., Coppola, G., Hilaire, P., Millet, C., Lemaître, A., Sagnes, I., Krebs, O., Lanco, L., Loredo, J.C., Antón, C., Somaschi, N., Senellart, P.: Reproducibility of high-performance quantum dot single-photon sources. ACS Photon. 7(4), 1050–1059 (2020)

Kück, S.: Single photon sources for absolute radiometry—a review about the current state of the art. Meas. Sens. 18, 100219 (2021)

doi: 10.1016/j.measen.2021.100219

Georgieva, H., López, M., Hofer, H., Kanold, N., Kaganskiy, A., Rodt, S., Reitzenstein, S., Kück, S.: Absolute calibration of a single-photon avalanche detector using a bright triggered single-photon source based on a quantum dot. Opt. Express 29(15), 23500–23507 (2021)

doi: 10.1364/OE.430680

Couteau, C., Barz, S., Durt, T., Gerrits, T., Huwer, J., Prevedel, R., Rarity, J., Shields, A., Weihs, G.: Applications of single photons to quantum communication and computing. Nat. Rev. Phys. 5, 326 (2023)

doi: 10.1038/s42254-023-00583-2

Couteau, C., Barz, S., Durt, T., Gerrits, T., Huwer, J., Prevedel, R., Rarity, J., Shields, A., Weihs, G.: Applications of single photons in quantum metrology, biology and the foundations of quantum physics. Nat. Rev. Phys. 5, 354 (2023)

doi: 10.1038/s42254-023-00589-w

Khalid, S., Laussy, F.P.: Perfect single-photon sources. Sci. Rep. 14, 2684 (2024)

doi: 10.1038/s41598-023-47585-9

Gaither-Ganim, M.B., Newlon, S.A., Anderson, M.G., Lee, B.: Organic molecule single-photon sources. Oxford Open Mater. Sci. 3, 1 (2024)

Guo, S., Germanis, S., Taniguchi, T., Watanabe, K., Withers, F., Luxmoore, I.J.: Source, electrically driven site-controlled single photon. ACS Photon. 10(8), 2549–2555 (2023)

doi: 10.1021/acsphotonics.3c00097

Castelletto, S., Boretti, A.: Perspective on solid-state single-photon sources in the infrared for quantum technology. Adv. Quantum Technol. 6, 2300145 (2023)

doi: 10.1002/qute.202300145

Lodahl, P., Ludwig, A., Warburton, R.J.: A deterministic source of single photons. Phys. Today 75(3), 44–50 (2022)

doi: 10.1063/PT.3.4962

Vannucci, L., Gregersen, N.: Highly efficient and indistinguishable single-photon sources via phonon-decoupled two-color excitation. Phys. Rev. B 107, 195306 (2023)

doi: 10.1103/PhysRevB.107.195306

Cao, X., Zopf, M., Ding, F.: Telecom wavelength single photon sources. J. Semicond. 40, 071901 (2019)

doi: 10.1088/1674-4926/40/7/071901

Senellart, P.: Semiconductor single-photon sources: progresses and applications. Photoniques 107, 40–43 (2021)

doi: 10.1051/photon/202110740

You, X., Zheng, M.Y., Chen, S., Liu, R.Z., Qin, J., Xu, M.C., Ge, Z.X., Chung, T.H., Qiao, Y.K., Jiang, Y.F., Zhong, H.S., Chen, M.C., Wang, H., He, Y.M., Xie, X.P., Li, H., You, L.X., Schneider, C., Yin, J., Chen, T.Y., Benyoucef, M., Huo, Y.H., Höfling, S., Zhang, Q., Lu, C.Y., Pan, J.W.: Quantum interference with independent single-photon sources over 300 km fiber. Adv. Photon. 4, 066003 (2022)

Ye, Y., Lin, X., Fang, W.: Room-temperature single-photon sources based on colloidal quantum dots: a review. Materials 16(24), 7684 (2023)

doi: 10.3390/ma16247684

Uppu, R., Pedersen, F.T., Wang, Y., Olesen, C.T., Papon, C., Zhou, X., Midolo, L., Scholz, S., Wieck, A.D., Ludwig, A., Lodahl, P.: Scalable integrated single-photon source. Sci. Adv. 6, eabc8268 (2020)

Manjavacas, A., GarcíadeAbajo, F.J.: Highly directional single-photon source. Nanophotonics 12(16), 3351–3358 (2023)

doi: 10.1515/nanoph-2023-0276

Martínez, A., Sanchis, P., Martí, J.: Mach-Zehnder interferometers in photonic crystals. Opt. Quant. Electron. 37, 77–93 (2005)

doi: 10.1007/s11082-005-1124-5

Perez, D., Gasulla, I., Fraile, F.J., Crudgington, L., Thomson, D.J., Khokhar, A.Z., Li, K., Cao, W., Mashanovich, G.Z., Capmany, J.: Silicon photonics rectangular universal interferometer. Laser Photon. Rev. 11, 1700219 (2017)

doi: 10.1002/lpor.201700219

Wang, M., Peng, J., Wang, W., Yang, M.: Photonic crystal fiber-based interferometer sensors. In: Peng, G.D. (ed.) Handbook of optical fibers. Springer, Singapore (2018)

Zhao, L., Liu, B., Wu, Y., Mao, Y., Sun, T., Zhao, D., Liu, Y., Liu, S.: Photonic crystal all-fiber Mach-Zehnder interferometer sensor based on phase demodulation. Opt. Fiber Technol. 53, 102059 (2019)

doi: 10.1016/j.yofte.2019.102059

Badoni, D., Gunnella, R., Salamon, A., Bonaiuto, V., Steglich, P.: Design and test of silicon photonic Mach-Zehnder interferometers for data transmission applications. In: 2020 Italian Conference on Optics and Photonics (ICOP). Parma, Italy, pp. 1–3 (2020)

Song, M., Steinmetz, J., Zhang, Y., Nauriyal, J., Lyons, K., Jordan, A.N., Cardenas, J.: Enhanced on-chip phase measurement by inverse weak value amplification. Nat. Commun. 12, 6247 (2021)

doi: 10.1038/s41467-021-26522-2

Zhu, C., Huang, J.: Microwave-photonic optical fiber interferometers for refractive index sensing with high sensitivity and a tunable dynamic range. Opt. Lett. 46, 2180–2183 (2021)

doi: 10.1364/OL.420618

Cherchi, M.: Autocorrective interferometers for photonic integrated circuits. In: Proceedings 12005, Smart Photonic and Optoelectronic Integrated Circuits 2022. 1200507 (2022)

Shen, J., Donnelly, D., Chakravarty, S.: Integrated photonic slow light Michelson interferometer bio sensor, Proceedings 12424, Integrated Optics: Devices, Materials, and Technologies XXVII; 124241B (2023)

Chaurasiya, R., Arora, D.: Photonic quantum computing. In: Kumar, A., Gill, S.S., Abraham, A. (eds.) Quantum and blockchain for modern computing systems: vision and advancements. Lecture notes on data engineering and communications technologies. Springer, Cham (2022)

Miller, D.A.B.: Self-configuring universal linear optical component. Photon. Res. 1, 1–15 (2013)

doi: 10.1364/PRJ.1.000001

Pérez, D., Gasulla, I., Capmany, J.: Programmable multifunctional integrated nanophotonics. Nanophotonics 7(8), 1351–1371 (2018)

doi: 10.1515/nanoph-2018-0051

Pérez, D., Gasulla, I., Capmany, J., Soref, R.A.: Reconfigurable lattice mesh designs for programmable photonic processors. Opt. Express 24, 12093–12106 (2016)

doi: 10.1364/OE.24.012093

Potter, R., Eisenman, W.: Infrared photodetectors: a review of operational detectors. Appl. Opt. 1(5), 567–574 (1962)

doi: 10.1364/AO.1.000567

Hadfield, R.: Single-photon detectors for optical quantum information applications. Nat. Photon. 3, 696–705 (2009)

doi: 10.1038/nphoton.2009.230

Marsili, F., Verma, V., Stern, J., Harrington, S., Lita, A.E., Gerrits, T., Vayshenker, I., Baek, B., Shaw, M.D., Mirin, R.P., Nam, S.W.: Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013)

Esmaeil Zadeh, I., Los, J.W.N., Gourgues, R.B.M., Chang, J., Elshaari, A.W., Zichi, J.R., van Staaden, Y.J., Swens, J.P.E., Kalhor, N., Guardiani, A., Meng, Y., Zou, K., Dobrovolskiy, S., Fognini, A.W., Schaart, D.R., Dalacu, D., Poole, P.J., Reimer, M.E., Hu, X., Pereira, S.F., Zwiller, V., Dorenbos, S.N.: Efficient single-photon detection with 7.7 ps time resolution for photon-correlation measurements. ACS Photon. 7, 1780–1787 (2020)

Perrenoud, M., Caloz, M., Amri, E., Autebert, C., Schönenberger, C., Zbinden, H., Bussières, F.: Operation of parallel SNSPDs at high detection rates. Supercond. Sci. Technol. 34, 024002 (2021)

doi: 10.1088/1361-6668/abc8d0

Stasi, L., Gras, G., Berrazouane, R., Bussieres, F.: High-efficiency and fast photon-number-resolving SNSPD. In: Quantum Information and Measurement VI 2021, F. Sciarrino, N. Treps, M. Giustina, and C. Silberhorn, eds., Technical Digest Series, Optica Publishing Group (2021)

Verma, V.B., Korzh, B., Walter, A.B., Lita, A.E., Briggs, R.M., Colangelo, M., Zhai, Y., Wollman, E.E., Beyer, A.D., Allmaras, J.P., Vora, H., Zhu, D., Schmidt, E., Kozorezov, A.G., Berggren, K.K., Mirin, R.P., Nam, S.W., Shaw, M.D.: Single-photon detection in the mid-infrared up to 10 μm wavelength using tungsten silicide superconducting nanowire detectors. APL Photon. 6, 056101 (2021)

Walsh, E.D., Jung, W., Lee, G.H., Efetov, D.K., Fong, K.C.: Josephson junction infrared single-photon detector. Science 372, 409–412 (2021)

doi: 10.1126/science.abf5539

Grünenfelder, F., Boaron, A., Resta, G.V., Perrenoud, M., Rusca, D., Barreiro, C., Houlmann, R., Sax, R., Stasi, L., El-Khoury, S., Hänggi, E., Bosshard, N., Bussières, F., Zbinden, H.: Fast single-photon detectors and real-time key distillation enable high secret-key-rate quantum key distribution systems. Nat. Photon. 17, 422–426 (2023)

Charaev, I., Bandurin, D.A., Bollinger, A.T., Phinney, I.Y., Drozdov, I., Colangelo, M., Butters, B.A., Taniguchi, T., Watanabe, K., He, X., Medeiros, O., Božović, I., Jarillo-Herrero, P., Berggren, K.K.: Single-photon detection using high-temperature superconductors. Nat. Nanotechnol. 18, 343–349 (2023)

doi: 10.1038/s41565-023-01325-2

Buckley, S.M., Stephens, M., Lehman, J.H.: Single photon detectors and metrology. ECS Trans. 109, 149 (2022)

doi: 10.1149/10903.0149ecst

Esmaeil Zadeh, I., Chang, J., Los, J.W.N., Gyger, S., Elshaari, A.W., Steinhauer, S., Dorenbos, S.N., Zwiller, V.: Superconducting nanowire single-photon detectors: a perspective on evolution, state-of-the-art, future developments, and applications. Appl. Phys. Lett. 118, 190502 (2021)

Hadfield, R.H., Leach, J., Fleming, F., Paul, D.J., Tan, C.H., Ng, J.S., Henderson, R.K., Buller, G.S.: Single-photon detection for long-range imaging and sensing. Optica 10, 1124–1141 (2023)

doi: 10.1364/OPTICA.488853

Dai, Y., Jia, K., Zhu, G., Li, H., Fei, Y., Guo, Y., Yuan, H., Wang, H., Jia, X., Zhao, Q., Kang, L., Chen, J., Zhu, S., Wu, P., Xie, Z., Zhang, L.: All-fiber device for single-photon detection. PhotoniX 4, 7 (2023)

Sharma, V.: Analysis of single photon detectors in differential phase shift quantum key distribution. Opt. Quant. Electron. 55, 888 (2023)

doi: 10.1007/s11082-023-05170-4

Martinez, N.J.D., Gehl, M., Derose, C.T., Starbuck, A.L., Pomerene, A.T., Lentine, A.L., Trotter, D.C., Davids, P.S.: Single photon detection in a waveguide-coupled Ge-on-Si lateral avalanche photodiode. Opt. Express 25, 16130–16139 (2017)

doi: 10.1364/OE.25.016130

Warburton, R.E., Intermite, G., Myronov, M., Allred, P., Leadley, D.R., Gallacher, K., Paul, D.J., Pilgrim, N.J., Lever, L.J.M., Ikonic, Z., Kelsall, R.W., Huante-Ceron, E., Knights, A.P., Buller, G.S.: Ge-on-Si single-photon avalanche diode detectors: design, modeling, fabrication, and characterization at wavelengths 1310 and 1550 nm. IEEE Trans. Electron Devices 60(11), 3807–3813 (2013)

Zhang, J., Itzler, M., Zbinden, H., Pan, J.W.: Advances in InGaAs/InP single-photon detector systems for quantum communication. Light Sci. Appl. 4, e286 (2015)

doi: 10.1038/lsa.2015.59

Comandar, L.C., Fröhlich, B., Dynes, J.F., Sharpe, A.W., Lucamarini, M., Yuan, Z.L., Penty, R.V., Shields, A.J.: Gigahertz-gated InGaAs/InP single-photon detector with detection efficiency exceeding 55% at 1550 nm. J. Appl. Phys. 117, 083109 (2015)

doi: 10.1063/1.4913527

Yan, Z., Hamel, D.R., Heinrichs, A.K., Jiang, X., Itzler, M.A., Jennewein, T.: An ultra low noise telecom wavelength free running single photon detector using negative feedback avalanche diode. Rev. Sci. Instrum. 83, 073105 (2012)

doi: 10.1063/1.4732813

Korzh, B., Walenta, N., Lunghi, T., Gisin, N., Zbinden, H.: Free-running InGaAs single photon detector with 1 dark count per second at 10% efficiency. Appl. Phys. Lett. 104, 081108 (2014)

doi: 10.1063/1.4866582

Covi, M., Pressl, B., Günthner, T., Laiho, K., Krapick, S., Silberhorn, C., Weihs, G.: Liquid-nitrogen cooled, free-running single-photon sensitive detector at telecommunication wavelengths. Appl. Phys. B 118, 489–495 (2015)

doi: 10.1007/s00340-015-6019-y

Weng, Q., An, Z., Zhang, B., Chen, P., Chen, X., Zhu, Z., Lu, W.: Quantum dot single-photon switches of resonant tunneling current for discriminating-photon-number detection. Sci. Rep. 5, 9389 (2015)

doi: 10.1038/srep09389

Li, H., Zhang, L., You, L., Yang, X., Zhang, W., Liu, X., Chen, S., Wang, Z., Xie, X.: Large-sensitive-area superconducting nanowire single-photon detector at 850 nm with high detection efficiency. Opt. Express 23, 17301–17308 (2015)

doi: 10.1364/OE.23.017301

Zhang, W.J., Li, H., You, L.X., He, Y.H., Zhang, L., Liu, X.Y., Yang, X.Y., Wu, J.J., Guo, Q., Chen, S.J., Wang, Z., Xie, X.M.: Superconducting nanowire single-photon detectors at a wavelength of 940 nm. AIP Adv. 5, 067129 (2015)

Yamashita, T., Waki, K., Miki, S., Kirkwood, R.A., Hadfield, R.H., Terai, H.: Superconducting nanowire single-photon detectors with non-periodic dielectric multilayers. Sci. Rep. 6, 35240 (2016)

doi: 10.1038/srep35240

Atikian, H.A., Eftekharian, A., Jafari Salim, A., Burek, M.J., Choy, J.T., Hamed Majedi, A., Lončar, M.: Superconducting nanowire single photon detector on diamond. Appl. Phys. Lett. 104, 122602 (2014)

doi: 10.1063/1.4869574

Tyler, N.A., Barreto, J., Villarreal-Garcia, G.E., Bonneau, D., Sahin, D., O’Brien, J.L., Thompson, M.G.: Modelling superconducting nanowire single photon detectors in a waveguide cavity. Opt. Express 24, 8797–8808 (2016)

doi: 10.1364/OE.24.008797

Arpaia, R., Ejrnaes, M., Parlato, L., Tafuri, F., Cristiano, R., Golubev, D., Sobolewski, R., Bauch, T., Lombardi, F., Pepe, G.P.: High-temperature superconducting nanowires for photon detection. Physica C Superconductivity Appl. 509, 16–21 (2015)

doi: 10.1016/j.physc.2014.09.017

Takesue, H., Dyer, S.D., Stevens, M.J., Verma, V., Mirin, R.P., Nam, S.W.: Quantum teleportation over 100 km of fiber using highly efficient superconducting nanowire single-photon detectors. Optica 2, 832–835 (2015)

doi: 10.1364/OPTICA.2.000832

Le Jeannic, H., Verma, V.B., Cavaillès, A., Marsili, F., Shaw, M.D., Huang, K., Morin, O., Nam, S.W., Laurat, J.: High-efficiency WSi superconducting nanowire single-photon detectors for quantum state engineering in the near infrared. Opt. Lett. 41, 5341–5344 (2016)

doi: 10.1364/OL.41.005341

Zhang, W., You, L., Li, H., Huang, J., Lv, C.L., Zhang, L., Liu, X.Y., Wu, J.J., Wang, Z., Xie, X.M.: NbN superconducting nanowire single photon detector with efficiency over 90% at 1550 nm wavelength operational at compact cryocooler temperature. Sci. China Phys. Mech. Astron. 60, 120314 (2017)

doi: 10.1007/s11433-017-9113-4

Zadeh, I.E., Los, J.W.N., Gourgues, R.B.M., Steinmetz, V., Bulgarini, G., Dobrovolskiy, S.M., Zwiller, V., Dorenbos, S.N.: Single-photon detectors combining high efficiency, high detection rates, and ultra-high timing resolution. APL Photon. 2, 111301 (2017)

doi: 10.1063/1.5000001

Wang, Q., Renema, J.J., Engel, A., de Dood, M.J.A.: Design of NbN superconducting nanowire single-photon detectors with enhanced infrared detection efficiency. Phys. Rev. Appl. 8, 034004 (2017)

doi: 10.1103/PhysRevApplied.8.034004

Vorobyov, V.V., Kazakov, A.Y., Soshenko, V.V., Korneev, A.A., Shalaginov, M.Y., Bolshedvorskii, S.V., Sorokin, V.N., Divochiy, A.V., Vakhtomin, Y.B., Smirnov, K.V., Voronov, B.M.: Superconducting detector for visible and near-infrared quantum emitters [Invited]. Opt. Mater. Express 7, 513–526 (2017)

doi: 10.1364/OME.7.000513

Miki, S., Yabuno, M., Yamashita, T., Terai, H.: Stable, high-performance operation of a fiber-coupled superconducting nanowire avalanche photon detector. Opt. Express 25, 6796–6804 (2017)

doi: 10.1364/OE.25.006796

Ma, F., Zheng, M.Y., Yao, Q., Xie, X.P., Zhang, Q., Pan, J.W.: 1.064-μm-band up-conversion single-photon detector. Opt. Express 25, 14558–14564 (2017)

doi: 10.1364/OE.25.014558

Pelc, J.S., Ma, L., Phillips, C.R., Zhang, Q., Langrock, C., Slattery, O., Tang, X., Fejer, M.M.: Long-wavelength-pumped upconversion single-photon detector at 1550 nm: performance and noise analysis. Opt. Express 19, 21445–21456 (2011)

doi: 10.1364/OE.19.021445

Hu, Q., Dam, J.S., Pedersen, C., Tidemand-Lichtenberg, P.: High-resolution mid-IR spectrometer based on frequency upconversion. Opt. Lett. 37, 5232–5234 (2012)

doi: 10.1364/OL.37.005232

Pelc, J.S., Kuo, P.S., Slattery, O., Ma, L., Tang, X., Fejer, M.M.: Dual-channel, single-photon upconversion detector at 1.3 μm. Opt. Express 20, 19075–19087 (2012)

doi: 10.1364/OE.20.019075

Pomarico, E., Sanguinetti, B., Thew, R., Zbinden, H.: Room temperature photon number resolving detector for infared wavelengths. Opt. Express 18, 10750–10759 (2010)

doi: 10.1364/OE.18.010750

Zheng, M.Y., Shentu, G.L., Ma, F., Zhou, F., Zhang, H.T., Dai, Y.Q., Xie, X., Zhang, Q., Pan, J.W.: Integrated four-channel all-fiber up-conversion single-photon-detector with adjustable efficiency and dark count. Rev. Sci. Instrum. 87, 093115 (2016)

doi: 10.1063/1.4963176

Inomata, K., Lin, Z., Koshino, K., Oliver, W.D., Tsai, J.S., Yamamoto, T., Nakamura, Y.: Single microwave-photon detector using an artificial Λ-type three-level system. Nat. Commun. 7, 12303 (2016)

doi: 10.1038/ncomms12303

Najafi, F., Marsili, F., Dauler, E., Molnar, R.J., Berggren, K.K.: Timing performance of 30-nm-wide superconducting nanowire avalanche photodetectors. Appl. Phys. Lett. 100, 152602 (2012)

doi: 10.1063/1.3703588

Heat, R.M.: Nano-optical observation of cascade switching in a parallel superconducting nanowire single photon detector. Appl. Phys. Lett. 104, 063503 (2014)

doi: 10.1063/1.4865199

Miller, A.J., Lita, A.E., Calkins, B., Vayshenker, I., Gruber, S.M., Nam, S.W.: Compact cryogenic self-aligning fiber-to-detector coupling with losses below one percent. Opt. Express 19, 9102–9110 (2011)

doi: 10.1364/OE.19.009102

Calkins, B., Mennea, P.L., Lita, A.E., Metcalf, B.J., Kolthammer, W.S., Lamas-Linares, A., Spring, J.B., Humphreys, P.C., Mirin, R.P., Gates, J.C., Smith, P.G.: High quantum-efficiency photon-number-resolving detector for photonic on-chip information processing. Opt. Express 21, 22657–22670 (2013)

doi: 10.1364/OE.21.022657

Höpker, J.F., Bartnick, M., Meyer-Scott, E., Thiele, F., Meier, T., Bartley, T., Krapick, S., Montaut, N.M., Santandrea, M., Herrmann, H., Lengeling, S., Ricken, R., Quiring, V., Lita, A.E., Verma, V.B., Gerrits, T., Nam, S.W., Silberhorn, C.: Towards integrated superconducting detectors on lithium niobate waveguides. Proc. SPIE 10358 (2017)

Lamas-Linares, A., Calkins, B., Tomlin, N.A., Gerrits, T., Lita, A.E., Beyer, J., Mirin, R.P., Woo Nam, S.: Nanosecond-scale timing jitter for single photon detection in transition edge sensors. Appl. Phys. Lett. 102, 231117 (2013)

Avenhaus, M., Laiho, K., Chekhova, M.V., Silberhorn, C.: Accessing higher order correlations in quantum optical states by time multiplexing. Phys. Rev. Lett. 104, 063602 (2010)

doi: 10.1103/PhysRevLett.104.063602

Thomas, O., Yuan, Z., Shields, A.: Practical photon number detection with electric field-modulated silicon avalanche photodiodes. Nat. Commun. 3, 644 (2012)

doi: 10.1038/ncomms1641

Yuan, Y., Dong, Q., Yang, B., Guo, F., Zhang, Q., Han, M., Huang, J.: Solution-processed nanoparticle super-float-gated organic field-effect transistor as un-cooled ultraviolet and infrared photon counter. Sci. Rep. 3, 2707 (2013)

doi: 10.1038/srep02707

Akhlaghi, M., Schelew, E., Young, J.: Waveguide integrated superconducting single-photon detectors implemented as near-perfect absorbers of coherent radiation. Nat. Commun. 6, 8233 (2015)

doi: 10.1038/ncomms9233

Sprengers, J.P., Gaggero, A., Sahin, D., Jahanmirinejad, S., Frucci, G., Mattioli, F., Leoni, R., Beetz, J., Lermer, M., Kamp, M., Höfling, S., Sanjines, R., Fiore, A.: Waveguide superconducting single-photon detectors for integrated quantum photonic circuits. Appl. Phys. Lett. 99, 181110 (2011)

Jahanmirinejad, S., Frucci, G., Mattioli, F., Sahin, D., Gaggero, A., Leoni, R., Fiore, A.: Photon-number resolving detector based on a series array of superconducting nanowires. Appl. Phys. Lett. 101, 072602 (2012)

doi: 10.1063/1.4746248

Reithmaier, G., Lichtmannecker, S., Reichert, T., Hasch, P., Müller, K., Bichler, M., Gross, R., Finley, J.J.: On-chip time resolved detection of quantum dot emission using integrated superconducting single photon detectors. Sci. Rep. 3, 1901 (2013)

doi: 10.1038/srep01901

Sahin, D., Gaggero, A., Weber, J.W., Agafonov, I., Verheijen, M.A., Mattioli, F., Beetz, J., Kamp, M., Hofling, S., van de Sanden, M.C.M., Leoni, R., Fiore, A.: Waveguide nanowire superconducting single-photon detectors fabricated on gaas and the study of their optical properties. IEEE J. Sel. Top. Quantum Electron. 21(3800210), 1–10 (2015)

Zhou, Z., Jahanmirinejad, S., Mattioli, F., Sahin, D., Frucci, G., Gaggero, A., Leoni, R., Fiore, A.: Superconducting series nanowire detector counting up to twelve photons. Opt. Express 22, 3475–3489 (2014)

doi: 10.1364/OE.22.003475

Kaniber, M., Flassig, F., Reithmaier, G., Gross, R., Finley, J.J.: Integrated superconducting detectors on semiconductors for quantum optics applications. Appl. Phys. B 122, 115 (2016)

doi: 10.1007/s00340-016-6376-1

Drummond, M., Barzik, M., Bird, J., Zhang, D.S., Lechene, C.P., Corey, D.P., Cunningham, L.L., Friedman, T.B.: Live-cell imaging of actin dynamics reveals mechanisms of stereocilia length regulation in the inner ear. Nat. Commun. 6, 6873 (2015)

doi: 10.1038/ncomms7873

Mattioli, F., Zhou, Z., Gaggero, A., Gaudio, R., Leoni, R., Fiore, A.: Photon-counting and analog operation of a 24-pixel photon number resolving detector based on superconducting nanowires. Opt. Express 24, 9067–9076 (2016)

doi: 10.1364/OE.24.009067

Li, J., Kirkwood, R.A., Baker, L.J., Bosworth, D., Erotokritou, K., Banerjee, A., Heath, R.M., Natarajan, C.M., Barber, Z.H., Sorel, M., Hadfield, R.H.: Nano-optical single-photon response mapping of waveguide integrated molybdenum silicide (MoSi) superconducting nanowires. Opt. Express 24, 13931–13938 (2016)

doi: 10.1364/OE.24.013931

Tanner, M.G., Alvarez, L.S.E., Jiang, W., Warburton, R.J., Barber, Z.H., Hadfield, R.H.: A superconducting nanowire single photon detector on lithium niobate. Nanotechnology 23, 505201 (2012)

doi: 10.1088/0957-4484/23/50/505201

Cavalier, P., Villégier, J.-C., Feautrier, P., Constancias, C., Morand, A.: Light interference detection on-chip by integrated SNSPD counters. AIP Adv. 1, 042120 (2011)

doi: 10.1063/1.3656744

Ferrari, S., Kahl, O., Kovalyuk, V., Goltsman, G.N., Korneev, A., Pernice, W.H.: Waveguide-integrated single- and multi-photon detection at telecom wavelengths using superconducting nanowires. Appl. Phys. Lett. 106, 151101 (2015)

doi: 10.1063/1.4917166

Kahl, O., Ferrari, S., Kovalyuk, V., Goltsman, G.N., Korneev, A., Pernice, W.H.P.: Waveguide integrated superconducting single-photon detectors with high internal quantum efficiency at telecom wavelengths. Sci. Rep. 5, 10941 (2015)

doi: 10.1038/srep10941

Schuck, C., Pernice, W.H.P., Tang, H.X.: NbTiN superconducting nanowire detectors for visible and telecom wavelengths single photon counting on Si

doi: 10.1063/1.4788931

Schuck, C., Guo, X., Fan, L., Ma, X., Poot, M., Tang, H.X.: Quantum interference in heterogeneous superconducting-photonic circuits on a silicon chip. Nat. Commun. 7, 10352 (2016)

doi: 10.1038/ncomms10352

Beyer, A.D., Briggs, R.M., Marsili, F., Cohen, J.D., Meenehan, S.M., Painter, O.J., Shaw, M.D.: Waveguide-coupled superconducting nanowire single-photon detectors. In: CLEO: 2015, OSA Technical Digest (online) (Optica Publishing Group) (2015)

Shainline, J.M., Buckley, S.M., Nader, N., Gentry, C.M., Cossel, K.C., Cleary, J.W., Popović, M., Newbury, N.R., Nam, S.W., Mirin, R.P.: Room-temperature-deposited dielectrics and superconductors for integrated photonics. Opt. Express 25, 10322–10334 (2017)

doi: 10.1364/OE.25.010322

Rath, P., Kahl, O., Ferrari, S., Sproll, F., Lewes-Malandrakis, G., Brink, D., Ilin, K., Siegel, M., Nebel, C., Pernice, W.: Superconducting single-photon detectors integrated with diamond nanophotonic circuits. Light Sci. Appl. 4, e338 (2015)

doi: 10.1038/lsa.2015.111

Eisaman, M.D., Fan, J., Migdall, A., Polyakov, S.V.: Single-photon sources and detectors. Rev. Sci. Instrum. 82, 071101 (2011)

doi: 10.1063/1.3610677

Natarajan, C.M., Tanner, M.G., Hadfield, R.H.: Superconducting nanowire single-photon detectors: physics and applications. Supercond. Sci. Technol. 25, 063001 (2012)

doi: 10.1088/0953-2048/25/6/063001

Melati, D., Melloni, A., Morichetti, F.: Real photonic waveguides: guiding light through imperfections. Adv. Opt. Photon. 6, 156–224 (2014)

doi: 10.1364/AOP.6.000156

Bazzan, M., Sada, C.: Optical waveguides in lithium niobate: recent developments and applications. Appl. Phys. Rev. 2, 040603 (2015)

doi: 10.1063/1.4931601

Kima, S., Yan, R.: Recent developments in photonic, plasmonic and hybrid nanowire waveguides. J. Mater. Chem. C 6, 11795 (2018)

doi: 10.1039/C8TC02981D

Saito, S., Tomita, I., Sotto, M., Debnath, K., Byers, J., Al-Attili, A.Z., Burt, D., Husain, M.K., Arimoto, H., Ibukuro, K., Charlton, M., Thomson, D.J., Zhang, W., Chen, B., Gardes, F.Y., Reed, G.T., Rutt, H.N.: Si photonic waveguides with broken symmetries: applications from modulators to quantum simulations. Jpn. J. Appl. Phys. 59, SO0801 (2020)

Katyba, G.M., Zaytsev, K.I., Dolganova, I.N., Chernomyrdin, N.V., Ulitko, V.E., Rossolenko, S.N., Shikunova, I.A., Kurlov, V.N.: Sapphire waveguides and fibers for terahertz applications. Prog. Cryst. Growth Charact. Mater. 67(3), 100523 (2021)

doi: 10.1016/j.pcrysgrow.2021.100523

Meng, Y., Chen, Y., Lu, L., Ding, Y., Cusano, A., Fan, J.A., Hu, Q., Wang, K., Xie, Z., Liu, Z., Yang, Y., Liu, Q., Gong, M., Xiao, Q., Sun, S., Zhang, M., Yuan, X., Ni, X.: Optical meta-waveguides for integrated photonics and beyond. Light Sci. Appl. 10, 235 (2021)

Chen, S., Zhuo, M.P., Wang, X.D., Wei, G.Q., Liao, L.S.: Optical waveguides based on one-dimensional organic crystals. PhotoniX 2, 2 (2021)

doi: 10.1186/s43074-021-00024-2

Urbonas, D., Mahrt, R.F., Stöferle, T.: Low-loss optical waveguides made with a high-loss material. Light Sci. Appl. 10, 15 (2021)

doi: 10.1038/s41377-020-00454-w

Hassan, H.M.I., Areed, N.F.F., El-Mikati, H.A., Hameed, M.F.O., Obayya, S.S.A.: Low loss hybrid plasmonic photonic crystal waveguide for optical communication applications. Opt. Quant. Electron. 54, 431 (2022)

doi: 10.1007/s11082-022-03806-5

Zejie, Y., Gao, H., Wang, Y., Yue, Y., Tsang, H.K., Sun, X., Dai, D.: Fundamentals and applications of photonic waveguides with bound states in the continuum. J. Semicond. 44(10), 101301 (2023)

doi: 10.1088/1674-4926/44/10/101301

Messner, A., Moor, D., Chelladurai, D., Svoboda, R., Smajic, J., Leuthold, J.: Plasmonic, photonic, or hybrid? Reviewing waveguide geometries for electro-optic modulators. APL Photon. 8, 100901 (2023)

doi: 10.1063/5.0159166

Wang, J., Dong, J.: Optical waveguides and integrated optical devices for medical diagnosis, health monitoring and light therapies. Sensors 20, 3981 (2020)

doi: 10.3390/s20143981

Wang, X., Li, Z., Lei, S.: Soft optical waveguides for biomedical applications. Wearable devices, and soft robotics: a review. Adv. Intel. Syst. 6, 2300482 (2024)

doi: 10.1002/aisy.202300482

Corrielli, G., Crespi, A., Geremia, R., Ramponi, R., Sansoni, L., Santinelli, A., Mataloni, P., Sciarrino, F., Osellame, R.: Rotated waveplates in integrated waveguide optics. Nat. Commun. 5, 4249 (2014)

Takesue, H., Tokura, Y., Fukuda, H., Tsuchizawa, T., Watanabe, T., Yamada, K., Itabashi, S.: Entanglement generation using silicon wire waveguide. Appl. Phys. Lett. 91, 201108 (2007)

Zhang, M., Feng, L.T., Zhou, Z.Y., Chen, Y., Wu, H., Li, M., Gao, S.M., Guo, G.P., Guo, G.C., Dai, D.X., Ren, X.F.: Generation of multiphoton quantum states on silicon. Light Sci. Appl. 8, 41 (2019)

Zhang, X., Bell, B.A., Mahendra, A., Xiong, C., Leong, P.H.W., Eggleton, B.J.: Integrated silicon nitride time-bin entanglement circuits. Opt. Lett. 43, 3469–3472 (2018)

doi: 10.1364/OL.43.003469

Lu, X., Li, Q., Westly, D.A., Moille, G., Singh, A., Anant, V., Srinivasan, K.: Chip-integrated visible-telecom entangled photon pair source for quantum communication. Nat. Phys. 15, 373–381 (2019)

doi: 10.1038/s41567-018-0394-3

Horn, R., Abolghasem, P., Bijlani, B.J., Kang, D., Helmy, A.S., Weihs, G.: Monolithic source of photon pairs. Phys. Rev. Lett. 108, 153605 (2012)

doi: 10.1103/PhysRevLett.108.153605

Wang, J., Santamato, A., Jiang, P., Bonneau, D., Engin, E., Silverstone, J.W., Lermer, M., Beetz, J., Kamp, M., Höfling, S., Tanner, M.G., Natarajan, C.M., Hadfield, R.H., Dorenbos, S.N., Zwiller, V., O’Brien, J.L., Thompson, M.G.: Gallium arsenide (GaAs) quantum photonic waveguide circuits. Opt. Commun. 327, 49–55 (2014)

Sprengers, J.P., Gaggero, A., Sahin, D., Jahanmirinejad, S., Frucci, G., Mattioli, F., Leoni, R., Beetz, J., Lermer, M., Kamp, M., Höfling, S., Sanjines, R., Fiore, A.: Waveguide superconducting single photon detectors for integrated quantum photonic circuits. Appl. Phys. Lett. 99, 181110 (2011)

Tanzilli, S., Tittel, W., De Riedmatten, H., Zbinden, H., Baldi, P., DeMicheli, M., Ostrowsky, D.B., Gisin, N.: PPLN waveguide for quantum communication. Eur. Phys. J. D 18, 155–160 (2002)

doi: 10.1140/epjd/e20020019

Abellan, C., Amaya, W., Domenech, D., Muñoz, P., Capmany, J., Longhi, S., Mitchell, M.W., Pruneri, V.: Quantum entropy source on an InP photonic integrated circuit for random number generation. Optica 3, 989–994 (2016)

doi: 10.1364/OPTICA.3.000989

Capmany, J., Gasulla, I., Pérez, D.: Microwave photonics: the programmable processor. Nat. Photon. 10, 6–8 (2016)

doi: 10.1038/nphoton.2015.254

Vandoorne, K., Mechet, P., Van Vaerenbergh, T., Fiers, M., Morthier, G., Verstraeten, D., Schrauwen, B., Dambre, J., Bienstman, P.: Experimental demonstration of reservoir computing on a silicon photonics chip. Nat. Commun. 5, 3541 (2014)

doi: 10.1038/ncomms4541

Brunner, D., Soriano, M. C., der Sande, G. V.: Eds., Photonic Reservoir Computing: Optical Recurrent Neural Networks. De Gruyter (2019)

Rafayelyan, M., Dong, J., Tan, Y., Krzakala, F., Gigan, S.: Large-scale optical reservoir computing for spatiotemporal chaotic systems prediction. Phys. Rev. X 10, 041037 (2020)

Nakajima, M., Tanaka, K., Hashimoto, T.: Scalable reservoir computing on coherent linear photonic processor. Commun. Phys. 4, 20 (2021)

doi: 10.1038/s42005-021-00519-1

Pierangeli, D., Marcucci, G., Conti, C.: Large-scale photonic ising machine by spatial light modulation. Phys. Rev. Lett. 122, 213902 (2019)

doi: 10.1103/PhysRevLett.122.213902

Okawachi, Y., Yu, M., Jang, J.K., Ji, X., Zhao, Y., Kim, B.Y., Lipson, M., Gaeta, A.L.: Demonstration of chip-based coupled degenerate optical parametric oscillators for realizing a nanophotonic spin-glass. Nat. Commun. 11, 4119 (2020)

doi: 10.1038/s41467-020-17919-6

Leonetti, M., Hormann, E., Leuzzi, L., Parisi, G., Ruocco, G.: Optical computation of a spin glass dynamics with tunable complexity. Proc. Natl. Acad. Sci. 118(21), e2015207118 (2021)

doi: 10.1073/pnas.2015207118

Wang, T., Ma, S.Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nat. Commun. 13, 123 (2022)

doi: 10.1038/s41467-021-27774-8

Yung, M.H., Gao, X., Huh, J.: Universal bound on sampling bosons in linear optics and its computational implications. Natl. Sci. Rev. 6(4), 719–729 (2019)

doi: 10.1093/nsr/nwz048

Triggiani, D., Facchi, P., Tamma, V.: Heisenberg scaling precision in the estimation of functions of parameters in linear optical networks. Phys. Rev. A 104, 062603 (2021)

doi: 10.1103/PhysRevA.104.062603

Hoch, F., Giordani, T., Spagnolo, N., Crespi, A., Osellame, R., Sciarrino, F.: Characterization of multimode linear optical networks. Adv. Photon. Nexus 2(1), 016007 (2023)

doi: 10.1117/1.APN.2.1.016007

Rahman, M.S.S., Yang, X., Li, J., Bai, B., Ozcan, A.: Universal linear intensity transformations using spatially incoherent diffractive processors. Light Sci. Appl. 12, 195 (2023)

doi: 10.1038/s41377-023-01234-y

Erhard, M., Krenn, M., Zeilinger, A.: Advances in high-dimensional quantum entanglement. Nat. Rev. Phys. 2(7), 365–381 (2020)

doi: 10.1038/s42254-020-0193-5

Cozzolino, D., Da Lio, B., Bacco, D., Oxenløwe, L.K.: High-dimensional quantum communication: benefits, progress, and future challenges. Adv. Quantum Technol. 2(12), 1900038 (2019)

doi: 10.1002/qute.201900038

Imany, P., Jaramillo-Villegas, J.A., Alshaykh, M.S., Lukens, J.M., Odele, O.D., Moore, A.J., Leaird, D.E., Qi, M., Weiner, A.M.: High-dimensional optical quantum logic in large operational spaces. npj Quantum Inf. 5(1), 59 (2019)

doi: 10.1038/s41534-019-0173-8

Reimer, C., Sciara, S., Roztocki, P., Islam, M., Romero Cortés, L., Zhang, Y., Fischer, B., Loranger, S., Kashyap, R., Cino, A., Chu, S.T., Little, B.E., Moss, D.J., Caspani, L., Munro, W.J., Azaña, J., Kues, M., Morandotti, R.: High-dimensional one-way quantum processing implemented on d-level cluster states. Nat. Phys. 15, 148–153 (2019)

Xavier, G.B., Lima, G.: Quantum information processing with space-division multiplexing optical fibres. Commun. Phys. 3(1), 9 (2020)

doi: 10.1038/s42005-019-0269-7

Leedumrongwatthanakun, S., Innocenti, L., Defienne, H., Juffmann, T., Ferraro, A., Paternostro, M., Gigan, S.: Programmable linear quantum networks with a multimode fibre. Nat. Photon. 14(3), 139–142 (2020)

doi: 10.1038/s41566-019-0553-9

Marrucci, L., Karimi, E., Slussarenko, S., Piccirillo, B., Santamato, E., Nagali, E., Sciarrino, F.: Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications. J. Opt. 13, 064001 (2011)

doi: 10.1088/2040-8978/13/6/064001

Loudon, R.: The Quantum Theory of Light. Clarendon Press, Oxford (1983)

Diamanti, E., Leverrier, A.: Distributing secret keys with quantum continuous variables: principle, security and implementations. Entropy 17(9), 6072–6092 (2015)

doi: 10.3390/e17096072

Rahimi-Keshari, S., Lund, A.P., Ralph, T.C.: What can quantum optics say about computational complexity theory? Phys. Rev. Lett. 114, 060501 (2015)

doi: 10.1103/PhysRevLett.114.060501

Hamilton, C.S., Kruse, R., Sansoni, L., Barkhofen, S., Silberhorn, C., Jex, I.: Gaussian boson sampling. Phys. Rev. Lett. 119(17), 170501 (2017)

doi: 10.1103/PhysRevLett.119.170501

Lund, A.P., Laing, A., Rahimikeshari, S., Rudolph, T., Obrien, J.L., Ralph, T.C.: Boson sampling from a Gaussian state. Phys. Rev. Lett. 113(10), 100502 (2014)

doi: 10.1103/PhysRevLett.113.100502

Bharti, K., Cervera-Lierta, A., Kyaw, T.H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J.S., Menke, T., Mok, W.K.: Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys. 94, 015004 (2022)

doi: 10.1103/RevModPhys.94.015004

Yanagimoto, R., Ng, E., Jankowski, M., Nehra, R., McKenna, T.P., Onodera, T., Wright, L.G., Hamerly, R., Marandi, A., Fejer, M.M., Mabuchi, H.: Mesoscopic ultrafast nonlinear optics-the emergence of multimode quantum non-Gaussian physics. Optica 11, 896–918 (2024)

doi: 10.1364/OPTICA.514075

Rakhubovsky, A.A., Moore, D.W., Filip, R.: Quantum non-Gaussian optomechanics and electromechanics. Prog. Quantum Electron. 93, 100495 (2024)

doi: 10.1016/j.pquantelec.2023.100495

Menicucci, N.C., van Loock, P., Gu, M., Weedbrook, C., Ralph, T.C., Nielsen, M.A.: Universal quantum computation with continuous-variable cluster states. Phys. Rev. Lett. 97, 110501 (2006)

doi: 10.1103/PhysRevLett.97.110501

Andersen, U.L., Neergaard-Nielsen, J.S., van Loock, P., Furusawa, A.: Hybrid discrete- and continuous-variable quantum information. Nat. Phys. 11(9), 713–719 (2015)

doi: 10.1038/nphys3410

Myers, C.R., Ralph, T.C.: Coherent state topological cluster state production. New J. Phys. 13(11), 115015 (2011)

doi: 10.1088/1367-2630/13/11/115015

Auger, J.M., Anwar, H., Gimeno-Segovia, M., Stace, T.M., Browne, D.E.: Fault-tolerant quantum computation with nondeterministic entangling gates. Phys. Rev. A 97(3), 5–9 (2018)

doi: 10.1103/PhysRevA.97.030301

Alexander, R.N., Wang, P., Sridhar, N., Chen, M., Pfister, O., Menicucci, N.C.: One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator. Phys. Rev. A 94, 032327 (2016)

doi: 10.1103/PhysRevA.94.032327

Larsen, M.V., Neergaard-Nielsen, J.S., Andersen, U.L.: Architecture and noise analysis of continuous-variable quantum gates using two-dimensional cluster states. Phys. Rev. A 102, 042608 (2020)

doi: 10.1103/PhysRevA.102.042608

Alexander, R.N., Yokoyama, S., Furusawa, A., Menicucci, N.C.: Universal quantum computation with temporal-mode bi-layer square lattices. Phys. Rev. A 97, 032302 (2018)

doi: 10.1103/PhysRevA.97.032302

Wang, P., Chen, M., Menicucci, N.C., Pfister, O.: Weaving quantum optical frequency combs into continuous-variable hyper-cubic cluster states. Phys. Rev. A 90(3), 032325 (2014)

doi: 10.1103/PhysRevA.90.032325

Wu, B.H., Alexander, R.N., Liu, S., Zhang, Z.: Quantum computing with multi-dimensional continuous-variable cluster states in a scalable photonic platform. Phys. Rev. Res. 2(2), 023138 (2020)

doi: 10.1103/PhysRevResearch.2.023138

Fukui, K., Asavanant, W., Furusawa, A.: Temporal-mode continuous-variable 3-dimensional cluster state for topologically-protected measurement-based quantum computation. Phys. Rev. A 102, 032614 (2020)

doi: 10.1103/PhysRevA.102.032614

Lund, A.P., Ralph, T.C., Haselgrove, H.L.: Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett. 100, 030503 (2008)

doi: 10.1103/PhysRevLett.100.030503

Rudolph, T.: Why I am optimistic about the silicon-photonic route to quantum computing. APL Photon. 2(3), 030901 (2017)

doi: 10.1063/1.4976737

Doerr, C.R., Okamoto, K.: Advances in silica planar lightwave circuits. J. Lightw. Technol. 24, 4763–4789 (2006)

doi: 10.1109/JLT.2006.885255

Coldren, L.A., Nicholes, S.C., Johansson, L., Ristic, S., Guzzon, R.S., Norberg, E.J., Krishnamachari, U.: High performance InP-based photonic ICs-A tutorial. J. Lightw. Technol 29, 554–570 (2011)

doi: 10.1109/JLT.2010.2100807

Soref, R.: The past, present, and future of silicon photonics. IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006)

doi: 10.1109/JSTQE.2006.883151

Bogaerts, W.: Design challenges in silicon photonics. IEEE J. Sel. Top. Quantum Electron. 20, 8202008 (2014)

doi: 10.1109/JSTQE.2013.2295882

Bogaerts, W., Baets, R., Dumon, P., Wiaux, V., Beckx, S., Taillaert, D., Luyssaert, B., Van Campenhout, J., Bienstman, P., Van Thourhout, D.: Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology. J. Lightw. Technol. 23, 401–412 (2005)

Smit, M.K., Leijtens, X., Ambrosius, H., Bente, E., van der Tol, J., Smalbrugge, B., de Vries, T., Geluk, E.J., Bolk, J., van Veldhoven, R., Augustin, L., Thijs, P., D’Agostino, D., Rabbani, H., Lawniczuk, K., Stopinski, S., Tahvili, S., Corradi, A., Kleijn, E., Dzibrou, D., Felicetti, M., Bitincka, E., Moskalenko, V., Zhao, J., Santos, R., Gilardi, G., Yao, W., Williams, K., Stabile, P., Kuindersma, P., Pello, J., Bhat, S., Jiao, Y., Heiss, D., Roelkens, G., Wale, M., Firth, P., Soares, F., Grote, N., Schell, M., Debregeas, H., Achouche, M., Gentner, J.L., Bakker, A., Korthorst, T., Gallagher, D., Dabbs, A., Melloni, A., Morichetti, F., Melati, D., Wonfor, A., Penty, R., Broeke, R., Musk, B., Robbins, D.: An introduction to InP-based generic integration technology. Semicond. Sci. Technol. 29, 083001 (2014)

Leinse, A., Heideman, R.G., Hoekman, M., Schreuder, F., Falke, F., Roeloffzen, C.G.H., Zhuang, L., Burla, M., Marpaung, D., Geuzebroek, D.H., Dekker, R., Klein, E.J., van Dijk, P.W.L., Oldenbeuving, R.M.: TriPleX waveguide platform: low-loss technology over a wide wavelength range. Proc. SPIE 8767, 87670E (2013)

Kish, F., Nagarajan, R., Welch, D., Evans, P., Rossi, J., Pleumeekers, J., Dentai, A., Kato, M., Corzine, S., Muthiah, R., Ziari, M., Schneider, R., Reffle, M., Butrie, T., Lambert, D., Missey, M., Lal, V., Fisher, M., Murthy, S., Salvatore, R., Demars, S., James, A., Joyner, C.: From visible light-emitting diodes to large-scale III-V photonic integrated circuits. Proc. IEEE 101, 2255–2270 (2013)

Heck, M.J.R., Bauters, J.F., Davenport, M.L., Doylend, J.K., Jain, S., Kurczveil, G., Srinivasan, S., Tang, Y., Bowers, J.E.: Hybrid silicon photonic integrated circuit technology. IEEE J. Sel. Top. Quantum Electron. 19, 6100117 (2013)

doi: 10.1109/JSTQE.2012.2235413

Sacher, W., Huang, Y., Lo, G.Q., Poon, J.K.S.: Multilayer silicon nitride-on-silicon integrated photonic platforms and devices. J. Lightw. Technol. 33, 901–910 (2015)

doi: 10.1109/JLT.2015.2392784

Chen, X., Milosevic, M.M., Stankovic, S., Reynolds, S., Bucio, T.D., Li, K., Thomson, D.J., Gardes, F., Reed, G.T.: The emergence of silicon photonics as a flexible technology platform. Proc. IEEE 106, 2101–2116 (2018)

doi: 10.1109/JPROC.2018.2854372

Smit, M., Williams, K., van der Tol, J.: Past, present, and future of InP-based photonic integration. APL Photon. 4, 050901 (2019)

doi: 10.1063/1.5087862

Miller, D.A.B.: Self-aligning universal beam coupler. Opt. Express 21, 6360–6370 (2013)

doi: 10.1364/OE.21.006360

Pai, S., Williamson, I.A.D., Hughes, T.W., Minkov, M., Miller, D.A.B.: Parallel programming of an arbitrary feedforward photonic network. IEEE J. Sel. Top. Quantum Electron. 25, 6100813 (2020)

Bogaerts, W., Pérez, D., Capmany, J., Miller, D.A.B., Poon, J., Englund, D., Morichetti, F., Melloni, A.: Programmable photonic circuits. Nature 586, 207–216 (2020)

doi: 10.1038/s41586-020-2764-0

Amanti, F., Andrini, G., Armani, F., Barbato, F., Bellani, V., Bonaiuto, V., Cammarata, S., Campostrini, M., Dao, T.H., De Matteis, F., Demontis, V., Donati, S., Di Giuseppe, G., Ditalia Tchernij, S., Fontana, A., Forneris, J., Frontini, L., Gunnella, R., Iadanza, S., Kaplan, A.E., Lacava, C., Liberali, V., Martini, L., Marzioni, F., Morescalchi, L., Pedreschi, E., Piergentili, P., Prete, D., Rigato, V., Roncolato, C., Rossella, F., Salvato, M., Sargeni, F., Shojaii, J., Spinella, F., Stabile, A., Toncelli, A., Vitali, V.: Integrated photonic passive building blocks on silicon-on-insulator platform. Photonics 11(6), 494 (2024)

Capmany, J., Perez, D.: Programmable Integrated Photonics. Oxford University Press (2020)

doi: 10.1093/oso/9780198844402.001.0001

Perez-Lopez, D.: Programmable integrated silicon photonics waveguide meshes: optimized designs and control algorithms. IEEE J. Sel. Top. Quantum Electron. 26, 8301312 (2020)

Harris, N.C., Carolan, J., Bunandar, D., Prabhu, M., Hochberg, M., Baehr-Jones, T., Fanto, M.L., Smith, A.M., Tison, C.C., Alsing, P.M., Englund, D.: Linear programmable nanophotonic processors. Optica 5, 1623–1631 (2018)

Harris, N.C., Bunandar, D., Pant, M., Steinbrecher, G.R., Mower, J., Prabhu, M., Baehr-Jones, T., Hochberg, M., Englund, D.: Large-scale quantum photonic circuits in silicon. Nanophotonics 5, 456–468 (2016)

Notaros, J., Mower, J., Heuck, M., Lupo, C., Harris, N.C., Steinbrecher, G.R., Bunandar, D., Baehr-Jones, T., Hochberg, M., Lloyd, S., Englund, D.: Programmable dispersion on a photonic integrated circuit for classical and quantum applications. Opt. Express 25, 21275–21285 (2017)

Ipronic Programmable Photonics. Programmable Photonics: What, why and when? Available at the website of ipronics.com, accessed, White paper (2023)

Micó. G., Bru, L., Pastor, D., Pérez, D., Munoz, P.: C-band linear propagation properties for a 300 nm film height Silicon Nitride photonics platform. In: European Conference on Integrated Optics 2017: Eindhoven, Netherlands (2017)

Giordani, T., Hoch, F., Carvacho, G., Spagnolo, N., Sciarrino, F.: Integrated photonics in quantum technologies. Riv. Nuovo Cim. 46, 71–103 (2023)

doi: 10.1007/s40766-023-00040-x

Mennea, P.L., Clements, W.R., Smith, D.H., Gates, J.C., Metcalf, B.J., Bannerman, R.H.S., Burgwal, R., Renema, J.J., Kolthammer, W.S., Walmsley, I.A., Smith, P.G.R.: Modular linear optical circuits. Optica 5, 1087–1090 (2018)

Taballione, C., Wolterink, T.A.W., Eckstein, A., Lugani, J., Grootjans, R.: [Formula: see text] programmable quantum photonic processor based on silicon nitride waveguides. In: Frontiers in Optics, JTu3A.58, Optical Society of America (2018)

Xie, Y., Geng, Z., Zhuang, L., Burla, M., Taddei, C., Hoekman, M., Leinse, A., Roeloffzen, C.G.H., Boller, K.J., Lowery, A.J.: Programmable optical processor chips: toward photonic RF filters with DSP-level flexibility and MHz-band selectivity. Nanophotonics 7, 421–454 (2017)

Hall, T.J., Hasan, M.: Universal discrete Fourier optics RF photonic integrated circuit architecture. Opt. Express 24, 7600–7610 (2016)

doi: 10.1364/OE.24.007600

Dyakonov, I.V., Pogorelov, I.A., Bobrov, I.B., Kalinkin, A.A., Straupe, S.S., Kulik, S.P., Dyakonov, P.V., Evlashin, S.A.: Reconfigurable photonics on a glass chip. Phys. Rev. Appl. 10, 044048 (2018)

doi: 10.1103/PhysRevApplied.10.044048

Shokraneh, F., Geoffroy-Gagnon, S., Nezami, M.S., Liboiron-Ladouceur, O.: A single layer neural network implemented by a [Formula: see text] MZI-based optical processor. IEEE Photon. J. 11, 4501612 (2019)

doi: 10.1109/JPHOT.2019.2952562

Lu, L., Zhou, L., Chen, J.: Programmable SCOW mesh silicon photonic processor for linear unitary operator. Micromachines 10, 646 (2019)

doi: 10.3390/mi10100646

Schaeff, C., Polster, R., Huber, M., Ramelow, S., Zeilinger, A.: Experimental access to higher-dimensional entangled quantum systems using integrated optics. Optica 2, 523–529 (2015)

doi: 10.1364/OPTICA.2.000523

Miller, D.A.B.: Waves, modes, communications, and optics: a tutorial. Adv. Opt. Photon. 11, 679 (2019)

doi: 10.1364/AOP.11.000679

Annoni, A., Guglielmi, E., Carminati, M., Ferrari, G., Sampietro, M., Miller, D.A.B., Melloni, A., Morichetti, F.: Unscrambling light-automatically undoing strong mixing between modes. Light Sci. Appl. 6, e17110 (2017)

doi: 10.1038/lsa.2017.110

Bogaerts, W., Rahim, A.: Programmable photonics: an opportunity for an accessible large-volume PIC ecosystem. IEEE J. Sel. Top. Quantum Electron. 26, 1–17 (2020)

doi: 10.1109/JSTQE.2020.2982980

Pérez-López, D., López, A., DasMahapatra, P., Capmany, J.: Multipurpose self-configuration of programmable photonic circuits. Nat. Commun. 11, 6359 (2020)

doi: 10.1038/s41467-020-19608-w

Peters, N., Altepeter, J., Jeffrey, E., Branning, D., Kwiat, P.: Precise creation, characterization, and manipulation of single optical qubits. Quantum Inf. Comput. 3, 503 (2003)

Luo, W., Cao, L., Shi, Y., Wan, L., Zhang, H., Li, S., Chen, G., Li, Y., Li, S., Wang, Y., Sun, S., Karim, M.F., Cai, H., Kwek, L.C., Liu, A.Q.: Recent progress in quantum photonic chips for quantum communication and internet. Light Sci. Appl. 12, 175 (2023)

Hwang, W.Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003)

doi: 10.1103/PhysRevLett.91.057901

Lo, H.K., Ma, X.F., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005)

doi: 10.1103/PhysRevLett.94.230504

Wang, X.B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005)

doi: 10.1103/PhysRevLett.94.230503

Semenenko, H., Sibson, P., Hart, A., Thompson, M.G., Rarity, J.G., Erven, C.: Chip-based measurement-device-independent quantum key distribution. Optica 7, 238–242 (2020)

doi: 10.1364/OPTICA.379679

Agnesi, C., Da Lio, B., Cozzolino, D., Cardi, L., Ben Bakir, B., Hassan, K., Della Frera, A., Ruggeri, A., Giudice, A., Vallone, G., Villoresi, P., Tosi, A., Rottwitt, K., Ding, Y., Bacco, D.: Hong-Ou-Mandel interference between independent III-V on silicon waveguide integrated lasers. Opt. Lett. 44, 271–274 (2019)

Ma, Y.J., Liu, Y., Guan, H., Gazman, A., Li, Q., Ding, R., Li, Y., Bergman, K., Baehr-Jones, T., Hochberg, M.: Symmetrical polarization splitter/rotator design and application in a polarization insensitive WDM receiver. Opt. Express 23, 16052–16062 (2015)

doi: 10.1364/OE.23.016052

Harris, N.C., Ma, Y., Mower, J., Baehr-Jones, T., Englund, D., Hochberg, M., Galland, C.: Efficient, compact and low loss thermo-optic phase shifter in silicon. Opt. Express 22, 10487–10493 (2014)

doi: 10.1364/OE.22.010487

Weigel, P.O., Zhao, J., Fang, K., Al-Rubaye, H., Trotter, D., Hood, D., Mudrick, J., Dallo, C., Pomerene, A.T., Starbuck, A.L., DeRose, C.T., Lentine, A.L., Rebeiz, G., Mookherjea, S.: Bonded thin film lithium niobate modulator on a silicon photonics platform exceeding 100 GHz 3-dB electrical modulation band-width. Opt. Express 26, 23728–23739 (2018)

Xu, P.P., Zheng, J., Doylend, J.K., Majumdar, A.: Low-loss and broadband nonvolatile phase-change directional coupler switches. ACS Photon. 6, 553–557 (2019)

doi: 10.1021/acsphotonics.8b01628

Peruzzo, A., Laing, A., Politi, A., Rudolph, T., O’Brien, J.L.: Multimode quantum interference of photons in multiport integrated devices. Nat. Commun. 2, 224 (2011)

doi: 10.1038/ncomms1228

Elshaari, A.W., Zadeh, I.E., Fognini, A., Reimer, M.E., Dalacu, D., Poole, P.J., Zwiller, V., Jöns, K.D.: On-chip single photon filtering and multiplexing in hybrid quantum photonic circuits. Nat. Commun. 8, 379 (2017)

Hong, S.H., Zhang, L., Wang, Y., Zhang, M., Xie, Y., Dai, D.: Ultralow-loss compact silicon photonic waveguide spirals and delay lines. Photon. Res. 10, 1–7 (2022)

doi: 10.1364/PRJ.437726

He, M., Xu, M., Ren, Y., Jian, J., Ruan, Z., Xu, Y., Gao, S., Sun, S., Wen, X., Zhou, L., Liu, L., Guo, C., Chen, H., Yu, S., Liu, L., Cai, X.: High-performance hybrid silicon and lithium niobate Mach-Zehnder modulators for 100 Gbit [Formula: see text] and beyond. Nat. Photon. 13, 359–364 (2019)

Metcalf, B.J., Spring, J.B., Humphreys, P.C., Thomas-Peter, N., Barbieri, M., Kolthammer, W.S., Jin, X.M., Langford, N.K., Kundys, D., Gates, J.C., Smith, B.J., Smith, P.G.R., Walmsley, I.A.: Quantum teleportation on a photonic chip. Nat. Photon. 8, 770–774 (2014)

Zhang, G., Haw, J.Y., Cai, H., Xu, F., Assad, S., Fitzsimons, J.F., Zhou, X., Zhang, Y., Yu, S., Wu, J., Ser, W., Kwek, L.C., Liu, A.Q.: An integrated silicon photonic chip platform for continuous-variable quantum key distribution. Nat. Photon. 13(12), 839–842 (2019)

doi: 10.1038/s41566-019-0504-5

Wei, K.J., Li, W., Tan, H., Li, Y., Min, H., Zhang, W.J., Li, H., You, L., Wang, Z., Jiang, X., Chen, T.Y., Liao, S.K., Peng, C.Z., Xu, F., Pan, J.W.: High-speed measurement-device-independent quantum key distribution with integrated silicon photonics. Phys. Rev. X 10, 031030 (2020)

Cao, L., Luo, W., Wang, Y.X., Zou, J., Yan, R.D., Cai, H., Zhang, Y., Hu, X.L., Jiang, C., Fan, W.J., Zhou, X.Q., Dong, B., Luo, X.S., Lo, G.Q., Wang, Y.X., Xu, Z.W., Sun, S.H., Wang, X.B., Hao, Y.L., Jin, Y.F., Kwong, D.L., Kwek, L.C., Liu, A.Q.: Chip-based measurement-device-independent quantum key distribution using integrated silicon photonic systems. Phys. Rev. Appl. 14, 011001 (2020)

Marchetti, R., Lacava, C., Carroll, L., Gradkowski, K., Minzioni, P.: Coupling strategies for silicon photonics integrated chips. Photon. Res. 7, 201–239 (2019)

doi: 10.1364/PRJ.7.000201

Cardenas, J., Poitras, C.B., Luke, K., Luo, L.W., Morton, P.A., Lipson, M.: High coupling efficiency etched facet tapers in silicon waveguides. IEEE Photon. Technol. Lett. 26, 2380–2382 (2014)

doi: 10.1109/LPT.2014.2357177

Dirac, P.: The Principles of Quantum Mechanics. Clarendon Press, Oxford (1930)

Kržič, A., Sharma, S., Spiess, C., Chandrashekara, U., Töpfer, S., Sauer, G., del Campo, L., Kopf, T., Petscharnig, S., Grafenauer, T., Lieger, R., Ömer, B., Pacher, C., Berlich, R., Peschel, T., Damm, C., Risse, S., Goy, M., Rieländer, D., Tünnermann, A., Steinlechner, F.: Towards metropolitan free-space quantum networks. npj Quantum Inf. 9, 95 (2023)

Bennett, C. H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proc. International Conference on Computers, Systems & Signal Processing. IEEE, Bangalore, 175–179 (1984)

Bennett, C.H., Bessette, F., Brassard, G., Salvail, L., Smolin, J.: Experimental quantum cryptography. J. Cryptol. 5, 3–28 (1992)

doi: 10.1007/BF00191318

Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)

doi: 10.1103/PhysRevLett.85.441

Ding, Y., Bacco, D., Dalgaard, K., Cai, X., Zhou, X., Rottwitt, K., Oxenlwe, L.: High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits. npj Quantum Inf. 3, 25 (2017)

doi: 10.1038/s41534-017-0026-2

Diamanti, E., Lo, H.K., Qi, B., Yuan, Z.: Practical challenges in quantum key distribution. npj Quantum Inf. 2, 16025 (2016)

doi: 10.1038/npjqi.2016.25

Peev, M., Pacher, C., Alléaume, R., Barreiro, C., Bouda, J., Boxleitner, W., Debuisschert, T., Diamanti, E., Dianati, M., Dynes, J.F., Fasel, S., Fossier, S., Fürst, M., Gautier, J.D., Gay, O., Gisin, N., Grangier, P., Happe, A., Hasani, Y., Hentschel, M., Hübel, H., Humer, G., Länger, T., Legré, M., Lieger, R., Lodewyck, J., Lorünser, T., Lütkenhaus, N., Marhold, A., Matyus, T., Maurhart, O., Monat, L., Nauerth, S., Page, J.B., Poppe, A., Querasser, E., Ribordy, G., Robyr, S., Salvail, L., Sharpe, A.W., Shields, A.J., Stucki, D., Suda, M., Tamas, C., Themel, T., Thew, R.T., Thoma, Y., Treiber, A., Trinkler, P., Tualle-Brouri, R., Vannel, F., Walenta, N., Weier, H., Weinfurter, H., Wimberger, I., Yuan, Z.L., Zbinden, H., Zeilinger, A.: The SECOQC quantum key distribution network in Vienna. New J. Phys. 11, 075001 (2009)

Stucki, D., Legré, M., Buntschu, F., Clausen, B., Felber, N., Gisin, N., Henzen, L., Junod, P., Litzistorf, G., Monbaron, P., Monat, L., Page, J.B., Perroud, D., Ribordy, G., Rochas, A., Robyr, S., Tavares, J., Thew, R., Trinkler, P., Ventura, S., Voirol, R., Walenta, N., Zbinden, H.: Long-term performance of the SwissQuantum quantum key distribution network in a field environment. New J. Phys. 13, 123001 (2011)

Avesani, M., Foletto, G., Padovan, M., Calderaro, L., Agnesi, C., Bazzani, E., Berra, F., Bertapelle, T., Picciariello, F., Santagiustina, F.B.L., Scalcon, D., Scriminich, A., Stanco, A., Vedovato, F., Vallone, G., Villoresi, P.: Deployment-ready quantum key distribution over a classical network infrastructure in Padua. J. Lightwave Technol. 40, 1658–1663 (2022)

Sasaki, M., Fujiwara, M., Ishizuka, H., Klaus, W., Wakui, K., Takeoka, M., Miki, S., Yamashita, T., Wang, Z., Tanaka, A., Yoshino, K., Nambu, Y., Takahashi, S., Tajima, A., Tomita, A., Domeki, T., Hasegawa, T., Sakai, Y., Kobayashi, H., Asai, T., Shimizu, K., Tokura, T., Tsurumaru, T., Matsui, M., Honjo, T., Tamaki, K., Takesue, H., Tokura, Y., Dynes, J.F., Dixon, A.R., Sharpe, A.W., Yuan, Z.L., Shields, A.J., Uchikoga, S., Legré, M., Robyr, S., Trinkler, P., Monat, L., Page, J.B., Ribordy, G., Poppe, A., Allacher, A., Maurhart, O., Länger, T., Peev, M., Zeilinger, A.: Field test of quantum key distribution in the Tokyo QKD network. Opt. Express 19, 10387–10409 (2011)

Chen, T.Y., Liang, H., Liu, Y., Cai, W.Q., Ju, L., Liu, W.Y., Wang, J., Yin, H., Chen, K., Chen, Z.B., Peng, C.Z., Pan, J.W.: Field test of a practical secure communication network with decoy-state quantum cryptography. Opt. Express 17, 6540–6549 (2009)

Wang, S., Chen, W., Yin, Z.Q., Li, H.W., He, D.Y., Li, Y.H., Zhou, Z., Song, X.T., Li, F.Y., Wang, D., Chen, H., Han, Y.G., Huang, J.Z., Guo, J.F., Hao, P.L., Li, M., Zhang, C.M., Liu, D., Liang, W.Y., Miao, C.H., Wu, P., Guo, G.C., Han, Z.F.: Field and long-term demonstration of a wide area quantum key distribution network. Opt. Express 22, 21739–21756 (2014)

Dynes, J.F., Wonfor, A., Tam, W.S., Sharpe, A.W., Shields, A.J.: Cambridge quantum network. npj Quantum Inf. 5, 101 (2019)

doi: 10.1038/s41534-019-0221-4

Wang, L.J., Zhang, K.Y., Wang, J.Y., Cheng, J., Yang, Y.H., Tang, S.B., Yan, D., Tang, Y.L., Liu, Z., Yu, Y.: Experimental authentication of quantum key distribution with post-quantum cryptography. npj Quantum Inf. 7, 67 (2021)

Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

doi: 10.1103/PhysRevLett.70.1895

Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)

doi: 10.1038/37539

Wehner, S., Elkouss, D., Hanson, R.: Quantum internet: a vision for the road ahead. Science 362, eaam9288 (2018)

doi: 10.1126/science.aam9288

Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

doi: 10.1103/PhysRevA.65.032302

Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)

doi: 10.1103/PhysRevA.68.042317

Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)

doi: 10.1103/PhysRevA.69.052319

Hu, J.Y., Yu, B., Jing, M.Y., Xiao, L.T., Jia, S.T., Qin, G.Q., Long, G.L.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5, e16144 (2016)

doi: 10.1038/lsa.2016.144

Zhang, W., Ding, D.S., Sheng, Y.B., Zhou, L., Shi, B.S., Guo, G.C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)

doi: 10.1103/PhysRevLett.118.220501

Zhu, F., Zhang, W., Sheng, Y., Huang, Y.: Experimental long-distance quantum secure direct communication. Sci. Bull. 62, 1519–1524 (2017)

doi: 10.1016/j.scib.2017.10.023

Qi, R.Y., Sun, Z., Lin, Z., Niu, P., Hao, W., Song, L., Huang, Q., Gao, J., Yin, L., Long, G.L.: Implementation and security analysis of practical quantum secure direct communication. Light Sci. Appl. 8, 22 (2019)

doi: 10.1038/s41377-019-0132-3

Zhang, H.R., Sun, Z., Qi, R., Yin, L., Long, G.L., Lu, J.: Realization of quantum secure direct communication over 100 km fiber with time-bin and phase quantum states. Light Sci. Appl. 11, 83 (2022)

doi: 10.1038/s41377-022-00769-w

Qi, Z.T., Li, Y., Huang, Y., Feng, J., Zheng, Y., Chen, X.: A 15-user quantum secure direct communication network. Light Sci. Appl. 10, 183 (2021)

doi: 10.1038/s41377-021-00634-2

Long, G.L., Pan, D., Sheng, Y.B., Xue, Q., Lu, J., Hanzo, L.: An evolutionary pathway for the quantum internet relying on secure classical repeaters. IEEE Netw. 36, 82–88 (2022)

doi: 10.1109/MNET.108.2100375

Orieux, A., Diamanti, E.: Recent advances on integrated quantum communications. J. Opt. 18, 083002 (2016)

doi: 10.1088/2040-8978/18/8/083002

Żukowski, M., Zeilinger, A., Horne, M., Weinfurter, H.: Quest for GHZ states. Acta Phys. Pol. 93, 187–95 (1998)

doi: 10.12693/APhysPolA.93.187

Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

doi: 10.1103/PhysRevA.59.1829

Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557 (1992)

doi: 10.1103/PhysRevLett.68.557

Hatakeyama, Y., Mizutani, A., Kato, G., Imoto, N., Tamaki, K.: Differential-phase-shift quantum-key-distribution protocol with a small number of random delays. Phys. Rev. A 95, 042301 (2017)

doi: 10.1103/PhysRevA.95.042301

Lucamarini, M., Yuan, Z.L., Dynes, J.F., Shields, A.J.: Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557, 400 (2018)

doi: 10.1038/s41586-018-0066-6

Wang, X.B., Yu, Z.W., Hu, X.L.: Twin-field quantum key distribution with large misalignment error. Phys. Rev. A 98, 062323 (2018)

doi: 10.1103/PhysRevA.98.062323

Liu, Y., Zhang, W.J., Jiang, C., Chen, J.P., Zhang, C., Pan, W.X., Ma, D., Dong, H., Xiong, J.M., Zhang, C.J., Li, H., Wang, R.C., Wu, J., Chen, T.Y., You, L., Wang, X.B., Zhang, Q., Pan, J.W.: Experimental twin-field quantum key distribution over 1000 km fiber distance. Phys. Rev. Lett. 130, 210801 (2023)

doi: 10.1103/PhysRevLett.130.210801

Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)

doi: 10.1103/PhysRevLett.88.057902

Grosshans, F., Van Assche, G., Wenger, J., Brouri, R., Cerf, N.J., Grangier, P.: Quantum key distribution using Gaussian-modulated coherent states. Nature 421, 238–241 (2003)

doi: 10.1038/nature01289

Ziebell, M., Persechino, M., Harris, N., Galland, C., Marris-Morini, D., Vivien, L., Diamanti, E., Grangier, P.: Towards on-chip continuous-variable quantum key distribution. In: Proc. European Conference on Lasers and Electro-Optics-European Quantum Electronics Conference 2015. Optica Publishing Group, Munich (2015)

Greenberger, D.M., Horne, M.A., Zeilinger, A.: Going beyond Bell’s theorem. In: Kafatos, M. (ed.) Bell’s theorem, quantum theory and conceptions of the universe, pp. 69–72. Kluwer Academic, Dordrecht (1989)

doi: 10.1007/978-94-017-0849-4_10

Zhao, Y., Zhang, R., Chen, W., Wang, X. B., Hu, J.: Creation of Greenberger-Horne-Zeilinger states with thousands of atoms by entanglement amplification. npj Quantum Inf. 7, 24 (2021)

doi: 10.1038/s41534-021-00364-8

Sibson, P., Kennard, J.E., Stanisic, S., Erven, C., O’Brien, J.L., Thompson, M.G.: Integrated silicon photonics for high-speed quantum key distribution. Optica 4, 172–177 (2017)

doi: 10.1364/OPTICA.4.000172

Gisin, N., Ribordy, G., Zbinden, H., Stucki, D., Brunner, N., Scarani, V.: Towards practical and fast quantum cryptography. arXiv preprint arXiv:quant-ph/0411022 (2004)

Dai, J.C., Zhang, L., Fu, X., Zheng, X., Yang, L.: Pass-block architecture for distributed-phase-reference quantum key distribution using silicon photonics. Opt. Lett. 45, 2014–2017 (2020)

doi: 10.1364/OL.388654

Sax, R., Boaron, A., Boso, G., Atzeni, S., Crespi, A., Grünenfelder, F., Rusca, D., Al-Saadi, A., Bronzi, D., Kupijai, S., Rhee, H., Osellame, R., Zbinden, H.: High-speed integrated QKD system. Photon. Res. 11(6), 1007–1014 (2023)

doi: 10.1364/PRJ.481475

Collins, R.J., Amiri, R., Fujiwara, M., Honjo, T., Shimizu, K., Tamaki, K., Takeoka, M., Andersson, E., Buller, G.S., Sasaki, M.: Experimental transmission of quantum digital signatures over 90 km of installed optical fiber using a differential phase shift quantum key distribution system. Opt. Lett. 41, 4883–4886 (2016)

doi: 10.1364/OL.41.004883

Sun, Q.C., Mao, Y.L., Chen, S.J., Zhang, W., Jiang, Y.F., Zhang, Y.B., Zhang, W.J., Miki, S., Yamashita, T., Terai, H., Jiang, X.: Entanglement swapping with independent sources over an optical-fiber network. Phys. Rev. A 95, 032306 (2017)

doi: 10.1103/PhysRevA.95.032306

Schmitt-Manderbach, T., Weier, H., Fürst, M., Ursin, R., Tiefenbacher, F., Scheidl, T., Perdigues, J., Sodnik, Z., Kurtsiefer, C., Rarity, J.G., Zeilinger, A.: Experimental demonstration of free-space decoy-state quantum key distribution over 144 km. Phys. Rev. Lett. 98, 010504 (2007)

doi: 10.1103/PhysRevLett.98.010504

Sun, S.H., Tang, G.Z., Li, C.Y., Liang, L.M.: Experimental demonstration of passive-decoy-state quantum key distribution with two independent lasers. Phys. Rev. A 94, 032324 (2016)

doi: 10.1103/PhysRevA.94.032324

Cañas, G., Vera, N., Cariñe, J., González, P., Cardenas, J., Connolly, P.W.R., Przysiezna, A., Gómez, E.S., Figueroa, M., Vallone, G., Villoresi, P., Ferreira da Silva, T., Xavier, G.B., Lima, G.: High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers. Phys. Rev. A 96, 022317 (2017)

doi: 10.1103/PhysRevA.96.022317

Lo, H.K., Curty, M., Tamaki, K.: Secure quantum key distribution. Nat. Photon. 8, 595 (2014)

doi: 10.1038/nphoton.2014.149

Moskovich, D.: An overview of the state of the art for practical quantum key distribution. arXive preprint arXiv:1504.05471v4 [quant-ph] (2015)

Bunandar, D., Lentine, A., Lee, C., Cai, H., Long, C.M., Boynton, N., Martinez, N., DeRose, C., Chen, C., Grein, M., Trotter, D., Starbuck, A., Pomerene, A., Hamilton, S., Wong, F.N.C., Camacho, R., Davids, P., Urayama, J., Englund, D.: Metropolitan quantum key distribution with silicon photonics. Phys. Rev. X 8, 021009 (2018)

Paraïso, T.K., De Marco, I., Roger, T., Marangon, D.G., Dynes, J.F., Lucamarini, M., Yuan, Z., Shields, A.J.: A modulator-free quantum key distribution transmitter chip. npj Quantum Inf. 5, 42 (2019)

doi: 10.1038/s41534-019-0158-7

Geng, W., Zhang, C., Zheng, Y., He, J., Zhou, C., Kong, Y.: Stable quantum key distribution using a silicon photonic transceiver. Opt. Express 27, 29045–29054 (2019)

doi: 10.1364/OE.27.029045

Paraïso, T.K., Roger, T., Marangon, D.G., De Marco, I., Sanzaro, M., Woodward, R.I., Dynes, J.F., Yuan, Z., Shields, A.J.: A photonic integrated quantum secure communication system. Nat. Photon. 15, 850–856 (2021)

doi: 10.1038/s41566-021-00873-0

Avesani, M., Calderaro, L., Schiavon, M., Stanco, A., Agnesi, C., Santamato, A., Zahidy, M., Scriminich, A., Foletto, G., Contestabile, G.: Full daylight quantum-key-distribution at 1550 nm enabled by integrated silicon photonics. npj Quantum Inf. 7, 93 (2021)

doi: 10.1038/s41534-021-00421-2

Zheng, X.D., Zhang, P., Ge, R., Lu, L., He, G., Chen, Q., Qu, F., Zhang, L., Cai, X., Lu, Y., Zhu, S., Wu, P., Ma, X.S.: Heterogeneously integrated, superconducting silicon-photonic platform for measurement-device-independent quantum key distribution. Adv. Photon. 3, 055002 (2021)

Elshaari, A.W., Pernice, W., Srinivasan, K., Benson, O., Zwiller, V.: Hybrid integrated quantum photonic circuits. Nat. Photon. 14, 285–298 (2020)

doi: 10.1038/s41566-020-0609-x

Xu, F., Chen, W., Wang, S., Yin, Z.Q., Zhang, Y., Liu, Y., Zhou, Z., Zhao, Y.B., Li, H.W., Liu, D., Han, Z.F., Guo, G.C.: Field experiment on a robust hierarchical metropolitan quantum cryptography network. Chin. Sci. Bull. 54, 2991–2997 (2009)

Fujiwara, M., Waseda, A., Nojima, R., Moriai, S., Ogata, W., Sasaki, M.: Unbreakable distributed storage with quantum key distribution network and password-authenticated secret sharing. Sci. Rep. 6, 28988 (2016)

doi: 10.1038/srep28988

Elliott, C., Colvin, A., Pearson, D., Pikalo, O., Schlafer, J., Yeh, H.: Current status of the DARPA quantum network. arXiv preprint arXiv:quant-ph/0503058v2 (2005)

Schiavon, M., Vallone, G., Villoresi, P.: Experimental realization of equiangular three-state quantum key distribution. Sci. Rep. 6, 30089 (2016)

doi: 10.1038/srep30089

Autebert, C., Trapateau, J., Orieux, A., Lemaître, A., Gomez-Carbonell, C., Diamanti, E., Zaquine, I., Ducci, S.: Multi-user quantum key distribution with entangled photons from an AlGaAs chip. Quantum Sci. Technol. 1, 01LT02 (2016)

Sun, W., Wang, L.J., Sun, X.X., Mao, Y., Yin, H.L., Wang, B.X., Chen, T.Y., Pan, J.W.: Experimental integration of quantum key distribution and gigabit-capable passive optical network. J. Appl. Phys. 123, 043105 (2018)

doi: 10.1063/1.5003342

Tang, G.Z., Sun, S.H., Feihu, X., Chen, H., Li, C.Y., Liang, L.M.: Experimental asymmetric plug-and-play measurement-device-independent quantum key distribution. Phys. Rev. A 94, 032326 (2016)

doi: 10.1103/PhysRevA.94.032326

Yin, H.L., Chen, T.Y., Yu, Z.W., Liu, H., You, L.X., Zhou, Y.H., Chen, S.J., Mao, Y., Huang, M.Q., Zhang, W.J., Chen, H., Li, M.J., Nolan, D., Zhou, F., Jiang, X., Wang, Z., Zhang, Q., Wang, X.B., Pan, J.W.: Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117, 190501 (2016)

Dynes, J., Tam, W.S., Plews, A., Fröhlich, B., Sharpe, A.W., Lucamarini, M., Yuan, Z., Radig, C., Straw, A., Edwards, T., Shields, A.J.: Ultra-high bandwidth quantum secured data transmission. Sci. Rep. 6, 35149 (2016)

doi: 10.1038/srep35149

Lee, C., Bunandar, D., Zhang, Z., Steinbrecher, G. R., Ben Dixon, P., Wong, F. N. C., Shapiro, J. H., Hamilton, S. A., Englund, D.: High-rate large-alphabet quantum key distribution over deployed telecom fiber. In: Conference on Lasers and Electro-Optics, OSA Technical Digest (online). Optica Publishing Group (2016)

Dynes, J.F., Kindness, S.J., Tam, S.W.-B., Plews, A., Sharpe, A.W., Lucamarini, M., Fröhlich, B., Yuan, Z.L., Penty, R.V., Shields, A.J.: Quantum key distribution over multicore fiber. Opt. Express 24, 8081–8087 (2016)

doi: 10.1364/OE.24.008081

Liao, S.K., Yong, H.L., Liu, C., Shentu, G.L., Li, D.D., Lin, J., Dai, H., Zhao, S.Q., Li, B., Guan, J.Y., Chen, W., Gong, Y.H., Li, Y., Lin, Z.H., Pan, G.S., Pelc, J.S., Fejer, M.M., Zhang, W.Z., Liu, W.Y., Yin, J., Ren, J.G., Wang, X.B., Zhang, Q., Peng, C.Z., Pan, J.W.: Long-distance free-space quantum key distribution in daylight towards inter-satellite communication. Nat. Photon. 11, 509–513 (2017)

Wang, L.J., Zou, K.H., Sun, W., Mao, Y., Zhu, Y.X., Yin, H.L., Chen, Q., Zhao, Y., Zhang, F., Chen, T.Y., Pan, J.W.: Long-distance copropagation of quantum key distribution and terabit classical optical data channels. Phys. Rev. A 95, 012301 (2017)

doi: 10.1103/PhysRevA.95.012301

Collins, R.J., Amiri, R., Fujiwara, M., Honjo, T., Shimizu, K., Tamaki, K., Takeoka, M., Sasaki, M., Andersson, E., Buller, G.S.: Experimental demonstration of quantum digital signatures over 43 dB channel loss using differential phase shift quantum key distribution. Sci. Rep. 7, 3235 (2017)

doi: 10.1038/s41598-017-03401-9

Roberts, G.L., Lucamarini, M., Yuan, Z.L., Dynes, J.F., Comandar, L.C., Sharpe, A.W., Shields, A.J., Curty, M., Puthoor, I.V., Andersson, E.: Experimental measurement-device-independent quantum digital signatures. Nat. Commun. 8, 1098 (2017)

doi: 10.1038/s41467-017-01245-5

Yin, H.L., Wang, W.L., Tang, Y.L., Zhao, Q., Liu, H., Sun, X.X., Zhang, W.J., Li, H., Puthoor, I.V., You, L.X., Andersson, E., Wang, Z., Liu, Y., Jiang, X., Ma, X., Zhang, Q., Curty, M., Chen, T.Y., Pan, J.W.: Experimental measurement-device-independent quantum digital signatures over a metropolitan network. Phys. Rev. A 95, 042338 (2017)

Kiktenko, E.O., Pozhar, N.O., Duplinskiy, A.V., Kanapin, A.A., Sokolov, A.S., Vorobey, S.S., Miller, A.V., Ustimchik, V.E., Anufriev, M.N., Trushechkin, A.T., Yunusov, R.R., Kurochkin, V.L., Kurochkin, Y.V., Fedorov, A.K.: Demonstration of a quantum key distribution network in urban fibre-optic communication lines. Quantum Electron. 47, 798 (2017)

doi: 10.1070/QEL16469

Pugh, C.J., Kaiser, S., Bourgoin, J.P., Jin, J., Sultana, N., Agne, S., Anisimova, E., Makarov, V., Choi, E., Higgins, B.L., Jennewein, T.: Airborne demonstration of a quantum key distribution receiver payload. Quantum Sci. Technol. 2, 024009 (2017)

doi: 10.1088/2058-9565/aa701f

Yin, J., Cao, Y., Li, Y.H., Liao, S.K., Zhang, L., Ren, J.G., Cai, W.Q., Liu, W.Y., Li, B., Dai, H., Li, G.B., Lu, Q.M., Gong, Y.H., Xu, Y., Li, S.L., Li, F.Z., Yin, Y.Y., Jiang, Z.Q., Li, M., Jia, J.J., Ren, G., He, D., Zhou, Y.L., Zhang, X.X., Wang, N., Chang, X., Zhu, Z.C., Liu, N.L., Chen, Y.A., Lu, C.Y., Shu, R., Peng, C.Z., Wang, J.Y., Pan, J.W.: Satellite-based entanglement distribution over 1200 kilometers. Science 356, 1140 (2017)

Liao, S.K., Lin, J., Ren, J.G., Liu, W.Y., Qiang, J., Yin, J., Li, Y., Shen, Q., Zhang, L., Liang, X.F., Yong, H.L., Li, F.Z., Yin, Y.Y., Cao, Y., Cai, W.Q., Zhang, W.Z., Jia, J.J., Wu, J.C., Chen, X.W., Zhang, S.C., Jiang, X.J., Wang, J.F., Huang, Y.M., Wang, Q., Ma, L., Li, L., Pan, G.S., Zhang, Q., Chen, Y.A., Lu, C.Y., Liu, N.L., Ma, X., Shu, R., Peng, C.Z., Wang, J.Y., Pan, J.W.: Space-to-ground quantum key distribution using a small-sized payload on Tiangong-2 Space Lab. Chin. Phys. Lett. 34, 090302 (2017)

Takenaka, H., Carrasco-Casado, A., Fujiwara, M., Kitamura, M., Sasaki, M., Toyoshima, M.: Satellite-to-ground quantum-limited communication using a 50-kg-class microsatellite. Nat. Photon. 11, 502–508 (2017)

doi: 10.1038/nphoton.2017.107

Liao, S.K., Cai, W.Q., Handsteiner, J., Liu, B., Yin, J., Zhang, L., Rauch, D., Fink, M., Ren, J.G., Liu, W.Y., Li, Y., Shen, Q., Cao, Y., Li, F.Z., Wang, J.F., Huang, Y.M., Deng, L., Xi, T., Ma, L., Hu, T., Li, L., Liu, N.L., Koidl, F., Wang, P., Chen, Y.A., Wang, X.B., Steindorfer, M., Kirchner, G., Lu, C.Y., Shu, R., Ursin, R., Scheidl, T., Peng, C.Z., Wang, J.Y., Zeilinger, A., Pan, J.W.: Satellite-relayed intercontinental quantum network. Phys. Rev. Lett. 120, 030501 (2018)

Fröhlich, B., Lucamarini, M., Dynes, J.F., Comandar, L.C., Tam, W.W., Plews, A., Sharpe, A.W., Yuan, Z., Shields, A.J.: Long-distance quantum key distribution secure against coherent attacks. Optica 4, 163–167 (2017)

doi: 10.1364/OPTICA.4.000163

Rosenberg, D., Harrington, J.W., Rice, P.R., Hiskett, P.A., Peterson, C.G., Hughes, R.J., Lita, A.E., Nam, S.W., Nordholt, J.E.: Long-distance decoy-state quantum key distribution in optical fiber. Phys. Rev. Lett. 98, 010503 (2007)

doi: 10.1103/PhysRevLett.98.010503

Peng, C.Z., Zhang, J., Yang, D., Gao, W.B., Ma, H.X., Yin, H., Zeng, H.P., Yang, T., Wang, X.B., Pan, J.W.: Experimental long-distance decoy-state quantum key distribution based on polarization encoding. Phys. Rev. Lett. 98, 010505 (2007)

doi: 10.1103/PhysRevLett.98.010505

Fang, X.T., Zeng, P., Liu, H., Zou, M., Wu, W., Tang, Y.L., Sheng, Y.J., Xiang, Y., Zhang, W., Li, H., Wang, Z., You, L., Li, M.J., Chen, H., Chen, Y.A., Zhang, Q., Peng, C.Z., Ma, X., Chen, T.Y., Pan, J.W.: Implementation of quantum key distribution surpassing the linear rate-transmittance bound. Nat. Photon. 14, 422–425 (2020)

Boaron, A., Boso, G., Rusca, D., Vulliez, C., Autebert, C., Caloz, M., Perrenoud, M., Gras, G., Bussières, F., Li, M.J., Nolan, D., Martin, A., Zbinden, H.: Secure quantum key distribution over 421 km of optical fiber. Phys. Rev. Lett. 121, 190502 (2018)

doi: 10.1103/PhysRevLett.121.190502

Qiu, J.: Quantum communications leap out of the lab. Nature 508, 441–442 (2014)

doi: 10.1038/508441a

Micius Quantum Communication Satellite (QUESS). Aerospace Technology. Available at the website of aerospace-technology.com/projects/micius-quantum-communication-satellite . Accessed 11 July (2024)

Nippon Telegraph and Telephone Corporation (NTT). Available at the website of group.ntt . Accessed 11 July (2024)

University of Geneva—Université de Genève. Available at the website of unige.ch . Accessed 11 July (2024)

ID Quantique. Available at the website of idquantique.com . Accessed 11 July (2024)

Pittaluga, M., Minder, M., Lucamarini, M., Sanzaro, M., Woodward, R.I., Li, M.J., Yuan, Z., Shields, A.J.: 600-km repeater-like quantum communications with dual-band stabilization. Nat. Photon. 15, 530–535 (2021)

doi: 10.1038/s41566-021-00811-0

Toshiba Europe. Available at the website of toshiba.co.uk/pages/uk . Accessed 11 July (2024)

BT Labs. Available at the website of atadastral.co.uk/bt/ . Accessed 11 July (2024)

Woodward, R. I., Dynes, J. F., Wright, P., White, C., Parker, R. C., Wonfor, A., Yuan, Z. L., Lord, A., Shields A. J.: Quantum key secured communications field trial for Industry 4.0. In: Optical Fiber Communication Conference (OFC) 2021. OSA Technical Digest (Optica Publishing Group, 2021), paper Th4H.4. (2021)

Quantum Xchange. Available at the website of quantumxc.com . Accessed 11 July (2024)

QuTech—Research institute for quantum computing and quantum internet. Available at the website of qutech.nl . Accessed 11 July (2024)

China Mobile Limited. Available at the website of chinamobileltd.com . Accessed 11 July (2024)

Quantum Network Facility, Brookhaven National Laboratory. Available at the website of bnl.gov/instrumentation/quantum/ . Accessed 11 July (2024)

Sukachev, D., Bhaskar, M.: Announcing the AWS Center for Quantum Networking, AWS Quantum Technologies Blog (21 JUN 2022). Available at the website of aws.amazon.com/blogs/quantum-computing/announcing-the-aws-center-for-quantum-networking/ . Accessed 12 July (2024)

Schmaltz, T., Becher, C., Endo, C., Becher, C., Schmidt, J., Krieg, L., Weymann, L., Shirinzadeh, S., Schmaltz, T.: Monitoring Report 1 - Quantum Communication (July 2024). Fraunhofer ISI (2024)

Müller, R., Greinert, F.: Quantentechnologien: Für Ingenieure, Berlin, Boston: De Gruyter Oldenbourg (2023)

Tian, Y., Zhang, Y., Liu, S., Wang, P., Lu, Z., Wang, X., Li, Y.: High-performance long-distance discrete-modulation continuous-variable quantum key distribution. Opt. Lett. 48, 2953–6 (2023)

doi: 10.1364/OL.492082

Zhang, Y., Bian, Y., Li, Z., Yu, S., Guo, H.: Continuous-variable quantum key distribution system: past, present, and future. Appl. Phys. Rev. 11 (2024)

Preskill, J.: Quantum computing and the entanglement frontier. arXiv preprint arXiv:1203.5813v3 [quant-ph] (2012)

Neill, C., Roushan, P., Kechedzhi, K., Boixo, S., Isakov, S.V., Smelyanskiy, V., Megrant, A., Chiaro, B., Dunsworth, A., Arya, K., Barends, R., Burkett, B., Chen, Y., Chen, Z., Fowler, A., Foxen, B., Giustina, M., Graff, R., Jeffrey, E., Huang, T., Kelly, J., Klimov, P., Lucero, E., Mutus, J., Neeley, M., Quintana, C., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Neven, H., Martinis, J.M.: A blueprint for demonstrating quantum supremacy with superconducting qubits. Science 360, 195–199 (2018)

Brod, D.J., Galvão, E.F., Crespi, A., Osellame, R., Spagnolo, N., Sciarrino, F.: Photonic implementation of boson sampling: a review. Adv. Photon. 1(3), 034001 (2019)

Zhu, H., Zou, J., Zhang, H., Shi, Y., Luo, S., Wang, N., Cai, H., Wan, L., Wang, B., Jiang, X., Thompson, J., Luo, X.S., Zhou, X.H., Xiao, L.M., Huang, W., Patrick, L., Gu, M., Kwek, L.C., Liu, A.Q.: Space-efficient optical computing with an integrated chip diffractive neural network. Nat. Commun. 13(1), 1–9 (2022)

Arora, S., Barak, B.: Computational Complexity: a Modern Approach. Cambridge University Press (2009)

Lund, A.P., Bremner, M.J., Ralph, T.C.: Quantum sampling problems, BosonSampling and quantum supremacy. npj Quantum Inf 3, 15 (2017)

doi: 10.1038/s41534-017-0018-2

Aaronson, S., Brod, D.J.: BosonSampling with lost photons. Phys. Rev. A 93, 012335 (2016)

doi: 10.1103/PhysRevA.93.012335

Leverrier, A., Garcia-Patron, R.: Analysis of circuit imperfections in bosonsampling. Quantum Inf. Comput. 15, 489–512 (2015)

Arkhipov, A.: BosonSampling is robust against small errors in the network matrix. Phys. Rev. A 92, 062326 (2015)

doi: 10.1103/PhysRevA.92.062326

Rahimi-Keshari, S., Ralph, T.C., Caves, C.M.: Sufficient conditions for efficient classical simulation of quantum optics. Phys. Rev. X 6, 021039 (2016)

Rohde, P.P., Ralph, T.C.: Error tolerance of the boson-sampling model for linear optics quantum computing. Phys. Rev. A 85, 022332 (2012)

doi: 10.1103/PhysRevA.85.022332

Wigner, E.P.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749 (1932)

doi: 10.1103/PhysRev.40.749

Husimi, K.: Some formal properties of the density matrix. Proc. Phys. Math. Soc. Jpn. 22, 264 (1940)

Kruse, R., Hamilton, C.S., Sansoni, L., Barkhofen, S., Silberhorn, C., Jex, I.: Detailed study of gaussian boson sampling. Phys. Rev. A 100(3), 032326 (2019)

doi: 10.1103/PhysRevA.100.032326

Jahangiri, S., Arrazola, J.M., Quesada, N., Killoran, N.: Point processes with Gaussian boson sampling. Phys. Rev. E 101, 022134 (2020)

doi: 10.1103/PhysRevE.101.022134

Banchi, L., Fingerhuth, M., Babej, T., Ing, C., Arrazola, J.M.: Molecular docking with Gaussian boson sampling. Sci. Adv. 6, eaax1950 (2020)

doi: 10.1126/sciadv.aax1950

Banchi, L., Quesada, N., Arrazola, J.M.: Training Gaussian boson sampling distributions. Phys. Rev. A 102, 012414 (2020)

doi: 10.1103/PhysRevA.102.012417

Jahangiri, S., Arrazola, J.M., Quesada, N., Delgado, A.: Quantum algorithm for simulating molecular vibrational excitations. Phys. Chem. Chem. Phys. 22, 25528–25537 (2020)

doi: 10.1039/D0CP03593A

Villalonga, B., Niu, M., Li, L., Neven, H., Platt, J.C., Smelyanskiy, V.N., Boixo, S.: Efficient approximation of experimental Gaussian boson sampling. arXiv preprint arXiv:2109.11525 (2021)

Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G.S.L., Buell, D.A., Burkett, B., Chen, Y., Chen, Z., Chiaro, B., Collins, R., Courtney, W., Dunsworth, A., Farhi, E., Foxen, B., Fowler, A., Gidney, C., Giustina, M., Graff, R., Guerin, K., Habegger, S., Harrigan, M.P., Hartmann, M.J., Ho, A., Hoffmann, M., Huang, T., Humble, T.S., Isakov, S.V., Jeffrey, E., Jiang, Z., Kafri, D., Kechedzhi, K., Kelly, J., Klimov, P.V., Knysh, S., Korotkov, A., Kostritsa, F., Landhuis, D., Lindmark, M., Lucero, E., Lyakh, D., Mandrà, S., McClean, J.R., McEwen, M., Megrant, A., Mi, X., Michielsen, K., Mohseni, M., Mutus, J., Naaman, O., Neeley, M., Neill, C., Niu, M.Y., Ostby, E., Petukhov, A., Platt, J.C., Quintana, C., Rieffel, E.G., Roushan, P., Rubin, N.C., Sank, D., Satzinger, K.J., Smelyanskiy, V., Sung, K.J., Trevithick, M.D., Vainsencher, A., Villalonga, B., White, T., Yao, Z.J., Yeh, P., Zalcman, A., Neven, H., Martinis, J.M.: Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019)

Morvan, A., Villalonga, B., Mi, X., Mandrà, S., Bengtsson, A., Klimov, P.V., Chen, Z., Hong, S., Erickson, C.: Phase transition in random circuit sampling. arXiv preprint arXiv:2304.11119 (2023)

Wu, Y., Bao, W.S., Cao, S., Chen, F., Chen, M.C., Chen, X., Chung, T.H., Deng, H., Du, Y., Fan, D., Gong, M., Guo, C., Guo, C., Guo, S., Han, L., Hong, L., Huang, H.L., Huo, Y.H., Li, L., Li, N., Li, S., Li, Y., Liang, F., Lin, C., Lin, J., Qian, H., Qiao, D., Rong, H., Su, H., Sun, L., Wang, L., Wang, S., Wu, D., Xu, Y., Yan, K., Yang, W., Yang, Y., Ye, Y., Yin, J., Ying, C., Yu, J., Zha, C., Zhang, C., Zhang, H., Zhang, K., Zhang, Y., Zhao, H., Zhao, Y., Zhou, L., Zhu, Q., Lu, C.Y., Peng, C.Z., Zhu, X., Pan, J.W.: Strong quantum computational advantage using a superconducting quantum processor. Phys. Rev. Lett. 127, 180501 (2021)

Zhu, Q., Cao, S., Chen, F., Chen, M.C., Chen, X., Chung, T.H., Deng, H., Du, Y., Fan, D., Gong, M., Guo, C., Guo, C., Guo, S., Han, L., Hong, L., Huang, H.L., Huo, Y.H., Li, L., Li, N., Li, S., Li, Y., Liang, F., Lin, C., Lin, J., Qian, H., Qiao, D., Rong, H., Su, H., Sun, L., Wang, L., Wang, S., Wu, D., Wu, Y., Xu, Y., Yan, K., Yang, W., Yang, Y., Ye, Y., Yin, J., Ying, C., Yu, J., Zha, C., Zhang, C., Zhang, H., Zhang, K., Zhang, Y., Zhao, H., Zhao, Y., Zhou, L., Lu, C.Y., Peng, C.Z., Zhu, X., Pan, J.W.: Quantum computational advantage via 60-qubit 24-cycle random circuit sampling. Sci. Bull. 67, 240–245 (2022)

Zlokapa, A., Villalonga, B., Boixo, S.L.D.A.: Boundaries of quantum supremacy via random circuit sampling. npj Quantum Inf. 9, 1 (2023)

doi: 10.1038/s41534-023-00703-x

Bouland, A., Fefferman, B., Nirkhe, C., Vazirani, U.: On the complexity and verification of quantum random circuit sampling. Nat. Phys. 15, 2 (2019)

doi: 10.1038/s41567-018-0318-2

Zhong, H.S., Li, Y., Li, W., Peng, L.C., Su, Z.E., Hu, Y., He, Y.M., Ding, X., Zhang, W., Li, H., Zhang, L., Wang, Z., You, L., Wang, X.L., Jiang, X., Li, L., Chen, Y.A., Liu, N.L., Lu, C.Y., Pan, J.W.: 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Phys. Rev. Lett. 121(25), 250505 (2018)

Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018)

doi: 10.22331/q-2018-08-06-79

Qi, H., Brod, D.J., Quesada, N., García-Patrón, R.: Regimes of classical simulability for noisy Gaussian Boson sampling. Phys. Rev. Lett. 124(10), 100502 (2020)

doi: 10.1103/PhysRevLett.124.100502

AbuGhanem, M.: Properties of some quantum computing models. Master’s Thesis, Ain Shams University (2019)

Huang, H.Y., Broughton, M., Cotler, J., Chen, S., Li, J., Mohseni, M., Neven, H., Babbush, R., Kueng, R., Preskill, J., McClean, J.R.: Quantum advantage in learning from experiments. Science 376, 6598 (2022)

doi: 10.1126/science.abn7293

Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. The MIT Press (2016)

Mohri, M., Rostamizadeh, A., Talwalkar, A.: Foundations of Machine Learning. The MIT Press (2018)

Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549, 195–202 (2017)

doi: 10.1038/nature23474

Broughton, M., Verdon, G., Mccourt, T., Martinez, A.J., Mohseni, M.: Tensorflow quantum: a software framework for quantum machine learning. arXiv preprint arXiv2003.02989 [quant-ph] (2021)

Benedetti, M., Coyle, B., Fiorentini, M., Lubasch, M., Rosenkranz, M.: Variational inference with a quantum computer. Phys. Rev. Appl. 16, 044057 (2021)

doi: 10.1103/PhysRevApplied.16.044057

Alvarez-Rodriguez, U., Sanz, M., Lamata, L., Solano, E.: Quantum artificial life in an IBM quantum computer. Sci. Rep. 8, 14793 (2018)

doi: 10.1038/s41598-018-33125-3

IBM, Exploring quantum use cases for chemicals and petroleum: changing how chemicals are designed and petroleum is refined. Available at the website of ibm.com/downloads/cas/BDGQRXOZ (2023)

Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017)

doi: 10.1038/nature23879

Aspuru-Guzik, A., Walther, P.: Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012)

doi: 10.1038/nphys2253

Gircha, A.I., Boev, A.S., Avchaciov, K., Fedichev, P.O., Fedorov, A.K.: Hybrid quantum-classical machine learning for generative chemistry and drug design. Sci. Rep. 13, 8250 (2023)

doi: 10.1038/s41598-023-32703-4

Degen, C.L., Reinhard, F., Cappellaro, P.: Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017)

doi: 10.1103/RevModPhys.89.035002

Yin, J., Li, Y.H., Liao, S.K., Yang, M., Cao, Y., Zhang, L., Ren, J.G., Cai, W.Q., Liu, W.Y., Li, S.L., Shu, R., Huang, Y.M., Deng, L., Li, L., Zhang, Q., Liu, N.L., Chen, Y.A., Lu, C.Y., Wang, X.B., Xu, F., Wang, J.Y., Peng, C.Z., Ekert, A.K., Pan, J.W.: Entanglement-based secure quantum cryptography over 1,120 kilometres. Nature 582, 501–505 (2020)

Yin, J., Cao, Y., Li, Y.H., Ren, J.G., Liao, S.K., Zhang, L., Cai, W.Q., Liu, W.Y., Li, B., Dai, H., Li, M., Huang, Y.M., Deng, L., Li, L., Zhang, Q., Liu, N.L., Chen, Y.A., Lu, C.Y., Shu, R., Peng, C.Z., Wang, J.Y., Pan, J.W.: Satellite-to-ground entanglement-based quantum key distribution. Phys. Rev. Lett. 119, 200501 (2017)

Ebadi, S., Keesling, A., Cain, M., Wang, T.T., Levine, H., Bluvstein, D., Semeghini, G., Omran, A., Liu, J.G., Samajdar, R., Luo, X.Z., Nash, B., Gao, X., Barak, B., Farhi, E., Sachdev, S., Gemelke, N., Zhou, L., Choi, S., Pichler, H., Wang, S.T., Greiner, M., Vuletić, V., Lukin, M.D.: Quantum optimization of maximum independent set using Rydberg atom arrays. Science 376, 1209 (2022)

Aspuru-Guzik, A., Dutoi, A.D., Love, P.J., Head-Gordon, M.: Simulated quantum computation of molecular energies. Science 309(5741), 1704–1707 (2005)

doi: 10.1126/science.1113479

Paesani, S., Gentile, A.A., Santagati, R., Wang, J., Wiebe, N., Tew, D.P., O’Brien, J.L., Thompson, M.G.: Experimental Bayesian quantum phase estimation on a silicon photonic chip. Phys. Rev. Lett. 118, 100503 (2017)

doi: 10.1103/PhysRevLett.118.100503

Nam, Y., Chen, J.-S., Pisenti, N.C., Wright, K., Delaney, C., Maslov, D., Brown, K.R., Allen, S., Amini, J.M., Apisdorf, J., Beck, K.M., Blinov, A., Chaplin, V., Chmielewski, M., Collins, C., Debnath, S., Hudek, K.M., Ducore, A.M., Keesan, M., Kreikemeier, S.M., Mizrahi, J., Solomon, P., Williams, M., Wong-Campos, J.D., Moehring, D., Monroe, C., Kim, J.: Ground-state energy estimation of the water molecule on a trapped-ion quantum computer. NPJ Quantum Inf. 6(1), 1–6 (2020)

doi: 10.1038/s41534-020-0259-3

Quantum Collaborators, G.A.: Hartree-fock on a superconducting qubit quantum computer. Science 369(6507), 1084–1089 (2020)

doi: 10.1126/science.abb9811

O’Malley, P.J., Babbush, R., Kivlichan, I.D., Romero, J., McClean, J.R., Barends, R., Kelly, J., Roushan, P., Tranter, A., Ding, N., Campbell, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Fowler, A.G., Jeffrey, E., Lucero, E., Megrant, A., Mutus, J.Y., Neeley, M., Neill, C., Quintana, C., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Coveney, P.V., Love, P.J., Neven, H., Aspuru-Guzik, A., Martinis, J.M.: Scalable quantum simulation of molecular energies. Phys. Rev. X 6(3), 031007 (2016)

McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of variational hybrid quantum-classical algorithms. New J. Phys. 18(2), 023023 (2016)

doi: 10.1088/1367-2630/18/2/023023

Sipser, M.: Introduction to the Theory of Computation, 3rd edn. Course Technology, Boston (2013)

Farhi, E., Goldstone, J., Gutmann, S.: A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028 [quant-ph] (2014)

Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. arXiv preprint arXiv:quant-ph/0001106 (2000)

Albash, T., Lidar, D.A.: Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018)

doi: 10.1103/RevModPhys.90.015002

Glover, F., Kochenberger, G., Hennig, R., Du, Y.: Quantum bridge analytics I: a tutorial on formulating and using QUBO models. Ann. Oper. Res. 17(4), 335–371 (2019)

Kadowaki, T., Nishimori, H.: Quantum annealing in the transverse Ising model. Phys. Rev. E 58(5), 5355 (1998)

doi: 10.1103/PhysRevE.58.5355

Ikeda, K., Nakamura, Y., Humble, T.S.: Application of quantum annealing to nurse scheduling problem. Sci. Rep. 9(1), 1–10 (2019)

doi: 10.1038/s41598-019-49172-3

Lucas, A.: Ising formulations of many NP problems. Front. Phys. 2, 5 (2014)

doi: 10.3389/fphy.2014.00005

Pelucchi, E., Fagas, G., Aharonovich, I., Englund, D., Figueroa, E., Gong, Q., Hannes, H., Liu, J., Lu, C.Y., Matsuda, N., Pan, J.W., Schreck, F., Sciarrino, F., Silberhorn, C., Wang, J., Jöns, K.D.: The potential and global outlook of integrated photonics for quantum technologies. Nat. Rev. Phys. 4, 194–208 (2022)

doi: 10.1038/s42254-021-00398-z

Nielsen, M.A.: Optical quantum computation using cluster states. Phys. Rev. Lett. 93, 040503 (2004)

doi: 10.1103/PhysRevLett.93.040503

Menicucci, N.C., Flammia, S.T., Pfister, O.: One-way quantum computing in the optical frequency comb. Phys. Rev. Lett. 101, 130501 (2008)

doi: 10.1103/PhysRevLett.101.130501

Quesada, N.: Franck-Condon factors by counting perfect matchings of graphs with loops. J. Chem. Phys. 150, 164113 (2019)

doi: 10.1063/1.5086387

Huh, J., Yung, M.H.: Vibronic Boson sampling: generalized Gaussian Boson sampling for molecular vibronic spectra at finite temperature. Sci. Rep. 7, 7462 (2017)

doi: 10.1038/s41598-017-07770-z

AbuGhanem, M.: Fast Universal Entangling Gate for Superconducting Quantum Computers. Elsevier, SSRN 4726035 (2024)

AbuGhanem, M.: Full quantum process tomography of a universal entangling gate on an IBM’s quantum computer. arXiv preprint arXiv:2402.06946 (2024)

Browne, D.E., Rudolph, T.: Resource-efficient linear optical quantum computation. Phys. Rev. Lett. 95, 010501 (2005)

doi: 10.1103/PhysRevLett.95.010501

Pant, M., Towsley, D., Englund, D., Guha, S.: Percolation thresholds for photonic quantum computing. Nat. Commun. 10, 1070 (2019)

doi: 10.1038/s41467-019-08948-x

Vigliar, C., Paesani, S., Ding, Y., Adcock, J.C., Wang, J., Morley-Short, S., Bacco, D., Oxenløwe, L.K., Thompson, M.G., Rarity, J.G., Laing, A.: Error-protected qubits in a silicon photonic chip. Nat. Phys. 17, 1137–1143 (2021)

doi: 10.1038/s41567-021-01333-w

Stipcevic, M.: Quantum random number generators and their applications in cryptography. In: Proc. SPIE 8375, Advanced Photon Counting Techniques VI. SPIE, Baltimore, 837504 (2012)

Williams, C.R.S., Salevan, J.C., Li, X., Roy, R., Murphy, T.E.: Fast physical random number generator using amplified spontaneous emission. Opt. Express 18, 23584–23597 (2010)

doi: 10.1364/OE.18.023584

Qi, B., Chi, Y.M., Lo, H.K., Qian, L.: High-speed quantum random number generation by measuring phase noise of a single-mode laser. Opt. Lett. 35, 312–314 (2010)

doi: 10.1364/OL.35.000312

Xu, F.H., Qi, B., Ma, X., Xu, H., Zheng, H., Lo, H.K.: Ultrafast quantum random number generation based on quantum phase fluctuations. Opt. Express 20, 12366–12377 (2012)

doi: 10.1364/OE.20.012366

Nie, Y.Q., Huang, L., Liu, Y., Payne, F., Zhang, J., Pan, J.W.: The generation of 68 Gbps quantum random number by measuring laser phase fluctuations. Rev. Sci. Instrum. 86, 063105 (2015)

doi: 10.1063/1.4922417

Liu, J.L., Yang, J., Li, Z., Su, Q., Huang, W., Xu, B., Guo, H.: 117 Gbits/s quantum random number generation with simple structure. IEEE Photon. Technol. Lett. 29, 283–286 (2017)

doi: 10.1109/LPT.2016.2639562

Gabriel, C., Wittmann, C., Sych, D., Dong, R., Mauerer, W., Andersen, U.L., Marquardt, C., Leuchs, G.: A generator for unique quantum random numbers based on vacuum states. Nat. Photon. 4, 711–715 (2010)

doi: 10.1038/nphoton.2010.197

Symul, T., Assad, S.M., Lam, P.K.: Real time demonstration of high bitrate quantum random number generation with coherent laser light. Appl. Phys. Lett. 98, 231103 (2011)

doi: 10.1063/1.3597793

Shi, Y.C., Chng, B., Kurtsiefer, C.: Random numbers from vacuum fluctuations. Appl. Phys. Lett. 109, 041101 (2016)

doi: 10.1063/1.4959887

Zheng, Z.Y., Zhang, Y., Huang, W., Yu, S., Guo, H.: 6 Gbps real-time optical quantum random number generator based on vacuum fluctuation. Rev. Sci. Instrum. 90, 043105 (2019)

doi: 10.1063/1.5078547

Zhou, Q., Valivarthi, R., John, C., Tittel, W.: Practical quantum random-number generation based on sampling vacuum fluctuations. Quantum Eng. 1, e8 (2019)

doi: 10.1002/que2.8

Haylock, B., Peace, D., Lenzini, F., Weedbrook, C., Lobino, M.: Multiplexed quantum random number generation. Quantum 3, 141 (2019)

doi: 10.22331/q-2019-05-13-141

Regazzoni, F., Amri, E., Burri, S., Rusca, D., Charbon, E.: A high speed integrated quantum random number generator with on-chip real-time randomness extraction. arXiv preprint arXiv:2102.06238 [quant-ph] (2021)

Bruynsteen, C., Gehring, T., Lupo, C., Bauwelinck, J., Yin, X.: 100-Gbit/s integrated quantum random number generator based on vacuum fluctuations. PRX Quantum 4, 010330 (2023)

doi: 10.1103/PRXQuantum.4.010330

Raffaelli, F., Sibson, P., Kennard, J.E., Mahler, D.H., Thompson, M.G., Matthews, J.C.F.: Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip. Opt. Express 26, 19730–19741 (2018)

doi: 10.1364/OE.26.019730

Freedman, S.J., Clauser, J.F.: Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972)

doi: 10.1103/PhysRevLett.28.938

Flamini, F., Magrini, L., Rab, A.S., Spagnolo, N., D’Ambrosio, V., Mataloni, P., Sciarrino, F., Zandrini, T., Crespi, A., Ramponi, R., Osellame, R.: Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining. Light Sci. Appl. 4, e354 (2015)

doi: 10.1038/lsa.2015.127

Ding, Y., Llewellyn, D., Faruque, I., Paesani, S., Bacco, D., Santagati, R., Qian, Y., Li, Y., Xiao, Y., Huber, M.: Demonstration of chip-to-chip quantum teleportation. In: Conference on Lasers Electro-Optics (CLEO). Optical Society of America, JTh5C.4 (2019)

Spagnolo, N., Vitelli, C., Aparo, L., Mataloni, P., Sciarrino, F., Crespi, A., Ramponi, R., Osellame, R.: Three-photon bosonic coalescence in an integrated tritter. Nat. Commun. 4, 1606 (2013)

doi: 10.1038/ncomms2616

Metcalf, B.J., Thomas-Peter, N., Spring, J.B., Kundys, D., Broome, M.A., Humphreys, P.C., Jin, X.M., Barbieri, M., Steven Kolthammer, W., Gates, J.C., Smith, B.J., Langford, N.K., Smith, P.G.R., Walmsley, I.A.: Multiphoton quantum interference in a multiport integrated photonic device. Nat. Commun. 4, 1356 (2013)

Spagnolo, N., Vitelli, C., Bentivegna, M., Brod, D.J., Crespi, A., Flamini, F., Giacomini, S., Milani, G., Ramponi, R., Mataloni, P., Osellame, R., Galvão, E.F., Sciarrino, F.: Experimental validation of photonic boson sampling. Nat. Photon. 8, 615–620 (2014)

doi: 10.1038/nphoton.2014.135

Giordani, T., Flamini, F., Pompili, M., Viggianiello, N., Spagnolo, N., Crespi, A., Osellame, R., Wiebe, N., Walschaers, M., Buchleitner, A., Sciarrino, F.: Experimental statistical signature of many-body quantum interference. Nat. Photon. 12, 173–178 (2018)

doi: 10.1038/s41566-018-0097-4

Agresti, I., Viggianiello, N., Flamini, F., Spagnolo, N., Crespi, A., Osellame, R., Wiebe, N., Sciarrino, F.: Pattern recognition techniques for Boson sampling validation. Phys. Rev. X 9, 011013 (2019)

Neville, A., Sparrow, C., Clifford, R., Johnston, E., Birchall, P.M., Montanaro, A., Laing, A.: Classical boson sampling algorithms with superior performance to near-term experiments. Nat. Phys. 13, 1153–1157 (2017)

doi: 10.1038/nphys4270

Crespi, A., Osellame, R., Ramponi, R., Giovannetti, V., Fazio, R., Sansoni, L., De Nicola, F., Sciarrino, F., Mataloni, P.: Anderson localization of entangled photons in an integrated quantum walk. Nat. Photon. 7, 322–328 (2013)

doi: 10.1038/nphoton.2013.26

Pitsios, I., Banchi, L., Rab, A.S., Bentivegna, M., Caprara, D., Crespi, A., Spagnolo, N., Bose, S., Mataloni, P., Osellame, R., Sciarrino, F.: Photonic simulation of entanglement growth and engineering after a spin chain quench. Nat. Commun. 8, 1569 (2017)

doi: 10.1038/s41467-017-01589-y

Crespi, A., Sansoni, L., Della Valle, G., Ciamei, A., Ramponi, R., Sciarrino, F., Mataloni, P., Longhi, S., Osellame, R.: Particle statistics affects quantum decay and Fano interference. Phys. Rev. Lett. 114, 090201 (2015)

doi: 10.1103/PhysRevLett.114.090201

Caruso, F., Crespi, A., Ciriolo, A.G., Sciarrino, F., Osellame, R.: Fast escape of a quantum walker from an integrated photonic maze. Nat. Commun. 7, 1682 (2016)

doi: 10.1038/ncomms11682

Biggerstaff, D.N., Heilmann, R., Zecevik, A.A., Gräfe, M., Broome, M.A., Fedrizzi, A., Nolte, S., Szameit, A., White, A.G., Kassal, I.: Enhancing coherent transport in a photonic network using controllable decoherence. Nat. Commun. 7, 11282 (2016)

doi: 10.1038/ncomms11282

Tang, H., Di Franco, C., Shi, Z.Y., He, T.S., Feng, Z., Gao, J., Sun, K., Li, Z.M., Jiao, Z.Q., Wang, T.Y., Kim, M.S., Jin, X.M.: Experimental quantum fast hitting on hexagonal graphs. Nat. Photon. 12, 754–758 (2018)

doi: 10.1038/s41566-018-0282-5

Poulios, K., Keil, R., Fry, D., Meinecke, J.D.A., Matthews, J.C.F., Politi, A., Lobino, M., Gräfe, M., Heinrich, M., Nolte, S., Szameit, A., O’Brien, J.L.: Quantum walks of correlated photon pairs in two-dimensional waveguide arrays. Phys. Rev. Lett. 112, 143604 (2014)

doi: 10.1103/PhysRevLett.112.143604

Santagati, R., Wang, J., Gentile, A.A., Paesani, S., Wiebe, N., McClean, J.R., Morley-Short, S., Shadbolt, P.J., Bonneau, D., Silverstone, J.W., Tew, D.P., Zhou, X., O’Brien, J.L., Thompson, M.G.: Witnessing eigenstates for quantum simulation of Hamiltonian spectra. Sci. Adv. 4, eaap9646 (2018)

doi: 10.1126/sciadv.aap9646

Photonics Market by Type (LED, Lasers, Detectors, Sensors and Imaging Devices, Optical Communication Systems & Networking components, Consumer Electronic & Devices), Application End-use Industry, and Region—Global Forecast to 2025, Photonics Market Report 2023, MarketsandMarkets Research Pvt. Ltd. Available at the website of marketsandmarkets.com/Market-Reports/photonics-market-88194993.html#utm_source=Globenewswire&utm_medium=Referal &utm_campaign=PaidPR . Accessed 21 July (2024)

Information processing at the speed of light.

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Muhammad AbuGhanem (M)

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