[1] A. Einstein, B. Podolsky, N. Rosen. Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev., 47, 777-780(1935).

[2] E. Schrödinger. Probability relations between separated systems. Math. Proc. Cambridge Philos. Soc., 32, 446-452(1936).

[3] J. S. Bell. On the Einstein–Podolsky–Rosen paradox. Phys., 1, 195-200(1964).

[4] B. Hensen et al. Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526, 682-686(2015).

[5] L. K. Shalm et al. Strong loophole-free test of local realism. Phys. Rev. Lett., 115, 250402(2015).

[6] M. Giustina et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett., 115, 250401(2015).

[7] N. Gisin et al. Quantum cryptography. Rev. Mod. Phys., 74, 145-195(2002).

[8] V. Giovannetti, S. Lloyd, L. Maccone. Quantum-enhanced measurements: beating the standard quantum limit. Science, 306, 1330-1336(2004).

[9] G. B. Lemos et al. Quantum imaging with undetected photons. Nature, 512, 409-412(2014).

[10] T. D. Ladd et al. Quantum computers. Nature, 464, 45-53(2010).

[11] I. M. Georgescu, S. Ashhab, F. Nori. Quantum simulation. Rev. Mod. Phys., 86, 153-185(2014).

[12] J.-W. Pan et al. Multiphoton entanglement and interferometry. Rev. Mod. Phys., 84, 777-838(2012).

[13] N. Gisin, R. Thew. Quantum communication. Nat. Photonics, 1, 165-171(2007).

[14] H. J. Kimble. Quantum internet. Nature, 453, 1023-1030(2008).

[15] H.-S. Zhong et al. Quantum computational advantage using photons. Science, 370, 1460-1463(2020).

[16] R. Raussendorf, H. J. Briegel. A one-way quantum computer. Phys. Rev. Lett., 86, 5188-5191(2001).

[17] P. Kok et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys., 79, 135-174(2007).

[18] J. L. O’Brien. Optical quantum computing. Science, 318, 1567-1570(2007).

[19] J. Wang et al. Integrated photonic quantum technologies. Nat. Photonics, 14, 273-284(2020).

[20] A. Politi et al. Silica-on-silicon waveguide quantum circuits. Science, 320, 646-649(2008).

[21] J. C. F. Matthews et al. Manipulation of multiphoton entanglement in waveguide quantum circuits. Nat. Photonics, 3, 346-350(2009).

[22] P. J. Shadbolt et al. Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nat. Photonics, 6, 45-49(2012).

[23] H. Takesue et al. Entanglement generation using silicon wire waveguide. Appl. Phys. Lett., 91, 201108(2007).

[24] J. W. Silverstone et al. On-chip quantum interference between silicon photon-pair sources. Nat. Photonics, 8, 104-108(2014).

[25] B. J. Smith et al. Phase-controlled integrated photonic quantum circuits. Opt. Express, 17, 13516-13525(2009).

[26] S. Tanzilli et al. PPLN waveguide for quantum communication. Eur. Phys. J. D, 18, 155-160(2002).

[27] H. Jin et al. On-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits. Phys. Rev. Lett., 113, 103601(2014).

[28] X. Lu et al. Chip-integrated visible-telecom entangled photon pair source for quantum communication. Nat. Phys., 15, 373-381(2019).

[29] X. Zhang et al. Integrated silicon nitride time-bin entanglement circuits. Opt. Lett., 43, 3469-3472(2018).

[30] R. Horn et al. Monolithic source of photon pairs. Phys. Rev. Lett., 108, 153605(2012).

[31] J. Wang et al. Gallium arsenide (GaAS) quantum photonic waveguide circuits. Opt. Commun., 327, 49-55(2014).

[32] P. Sibson et al. Chip-based quantum key distribution. Nat. Commun., 8, 13984(2017).

[33] H. Semenenko et al. Chip-based measurement-device-independent quantum key distribution. Optica, 7, 238-242(2020).

[34] M. A. Ciampini et al. Path-polarization hyperentangled and cluster states of photons on a chip. Light Sci. Appl., 5, e16064(2016).

[35] R. Santagati et al. Witnessing eigenstates for quantum simulation of Hamiltonian spectra. Sci. Adv., 4, eaap9646(2018).

[36] J. Wang et al. Experimental quantum Hamiltonian learning. Nat. Phys., 13, 551-555(2017).

[37] J. C. Adcock et al. Advances in silicon quantum photonics. IEEE J. Sel. Top. Quantum Electron., 27, 6700224(2021).

[38] A. Aspect, P. Grangier, G. Roger. Experimental realization of Einstein–Podolsky–Rosen–Bohm Gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett., 49, 91-94(1982).

[39] D. Bouwmeester et al. Observation of three-photon Greenberger–Horne–Zeilinger entanglement. Phys. Rev. Lett., 82, 1345-1349(1999).

[40] D. Bouwmeester et al. Experimental quantum teleportation. Nature, 390, 575-579(1997).

[41] D. Dai et al. Polarization management for silicon photonic integrated circuits. Laser Photonics Rev., 7, 303-328(2013).

[42] N. Matsuda et al. A monolithically integrated polarization entangled photon pair source on a silicon chip. Sci. Rep., 2, 817(2012).

[43] J. Wang et al. Multidimensional quantum entanglement with large-scale integrated optics. Science, 360, 285-291(2018).

[44] X. Qiang et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photonics, 12, 534-539(2018).

[45] L.-T. Feng et al. On-chip transverse-mode entangled photon pair source. NPJ Quantum Inf., 5, -2(2019).

[46] A. Mohanty et al. Quantum interference between transverse spatial waveguide modes. Nat. Commun., 8, 14010(2017).

[47] A. Mair et al. Entanglement of the orbital angular momentum states of photons. Nature, 412, 313-316(2001).

[48] R. Fickler et al. Quantum entanglement of high angular momenta. Science, 338, 640-643(2012).

[49] M. Malik et al. Multi-photon entanglement in high dimensions. Nat. Photonics, 10, 248-252(2016).

[50] A. Babazadeh et al. High-dimensional single-photon quantum gates: concepts and experiments. Phys. Rev. Lett., 119, 180510(2017).

[51] M. Kues et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature, 546, 622-626(2017).

[52] L. Olislager et al. Frequency-bin entangled photons. Phys. Rev. A, 82, 013804(2010).

[53] L. Olislager et al. Creating and manipulating entangled optical qubits in the frequency domain. Phys. Rev. A, 89, 052323(2014).

[54] F. Kaneda, P. G. Kwiat. High-efficiency single-photon generation via large-scale active time multiplexing. Sci. Adv., 5, eaaw8586(2019).

[55] X. Guo et al. Parametric down-conversion photon-pair source on a nanophotonic chip. Light Sci. Appl., 6, e16249-e16249(2017).

[56] Y. Zhang et al. Dual-pump approach to photon-pair generation: demonstration of enhanced characterization and engineering capabilities. Opt. Express, 27, 19050-19061(2019).

[57] B. Fang et al. State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing. Opt. Express, 21, 2707-2717(2013).

[58] S. Signorini et al. Intermodal four-wave mixing in silicon waveguides. Photonics Res., 6, 805-814(2018).

[59] S. Paesani et al. Near-ideal spontaneous photon sources in silicon quantum photonics. Nat. Commun., 11, 2505(2020).

[60] Z. Vernon, M. Liscidini, J. E. Sipe. No free lunch: the trade-off between heralding rate and efficiency in microresonator-based heralded single photon sources. Opt. Lett., 41, 788-791(2016).

[61] Z. Vernon et al. Truly unentangled photon pairs without spectral filtering. Opt. Lett., 42, 3638-3641(2017).

[62] D. Llewellyn et al. Chip-to-chip quantum teleportation and multi-photon entanglement in silicon. Nat. Phys., 16, 148-153(2020).

[63] J. B. Christensen et al. Engineering spectrally unentangled photon pairs from nonlinear microring resonators by pump manipulation. Opt. Lett., 43, 859-862(2018).

[64] Y. Liu et al. High-spectral-purity photon generation from a dual-interferometer-coupled silicon microring. Opt. Lett., 45, 73-76(2020).

[65] B. M. Burridge et al. High spectro-temporal purity single-photons from silicon micro-racetrack resonators using a dual-pulse configuration. Opt. Lett., 45, 4048-4051(2020).

[66] P. Walther et al. Experimental one-way quantum computing. Nature, 434, 169-176(2005).

[67] J. Wang et al. Chip-to-chip quantum photonic interconnect by path-polarization interconversion. Optica, 3, 407-413(2016).

[68] L.-T. Feng et al. On-chip coherent conversion of photonic quantum entanglement between different degrees of freedom. Nat. Commun., 7, 11985(2016).

[69] J. T. Barreiro, T.-C. Wei, P. G. Kwiat. Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys., 4, 282-286(2008).

[70] M. Fiorentino, F. N. C. Wong. Deterministic controlled-not gate for single-photon two-qubit quantum logic. Phys. Rev. Lett., 93, 070502(2004).

[71] X.-L. Wang et al. 18-qubit entanglement with six photons’ three degrees of freedom. Phys. Rev. Lett., 120, 260502(2018).

[72] C. Reimer et al. High-dimensional one-way quantum processing implemented on d-level cluster states. Nat. Phys., 15, 148-153(2019).

[73] N. D. Mermin. What’s wrong with these elements of reality?. Phys. Today, 43, 9-11(1990).

[74] M. Gimeno-Segovia et al. From three-photon Greenberger–Horne–Zeilinger states to ballistic universal quantum computation. Phys. Rev. Lett., 115, 020502(2015).

[75] Z.-D. Li et al. Experimental quantum repeater without quantum memory. Nat. Photonics, 13, 644-648(2019).

[76] H.-S. Zhong et al. 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Phys. Rev. Lett., 121, 250505(2018).

[77] J. C. Adcock et al. Programmable four-photon graph states on a silicon chip. Nat. Commun., 10, 3528(2019).

[78] S. Paesani et al. Generation and sampling of quantum states of light in a silicon chip. Nat. Phys., 15, 925-929(2019).

[79] M. Zhang et al. Generation of multiphoton quantum states on silicon. Light Sci. Appl., 8, 41(2019).

[80] L.-T. Feng et al. Observation of nonlocal quantum interference between the origins of a four-photon state in a silicon chip(2021).

[81] C. Reimer et al. Generation of multiphoton entangled quantum states by means of integrated frequency combs. Science, 351, 1176-1180(2016).

[82] C. Vigliar et al. Error protected qubits in a silicon photonic chip. Nat. Phys., 17, 1137-1143(2021).

[83] M. Erhard, M. Krenn, A. Zeilinger. Advances in high-dimensional quantum entanglement. Nat. Rev. Phys., 2, 365-381(2020).

[84] D. Collins et al. Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett., 88, 040404(2002).

[85] N. J. Cerf et al. Security of quantum key distribution using d-level systems. Phys. Rev. Lett., 88, 127902(2002).

[86] B. P. Lanyon et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys., 5, 134-140(2009).

[87] C. Schaeff et al. Experimental access to higher-dimensional entangled quantum systems using integrated optics. Optica, 2, 523-529(2015).

[88] W. R. Clements et al. Optimal design for universal multiport interferometers. Optica, 3, 1460-1465(2016).

[89] L. Lu et al. Three-dimensional entanglement on a silicon chip. NPJ Quantum Inf., 6, 30(2020).

[90] X. Chen et al. A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip. Nat. Commun., 12, 2712(2021).

[91] S. Paesani et al. Experimental Bayesian quantum phase estimation on a silicon photonic chip. Phys. Rev. Lett., 118, 100503(2017).

[92] A. Peruzzo et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun., 5, 4213(2014).

[93] A. H. Atabaki et al. Integrating photonics with silicon nanoelectronics for the next generation of systems on a chip. Nature, 556, 349-354(2018).

[94] N. C. Harris et al. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photonics, 11, 447-452(2017).

[95] D. J. Moss et al. New CMOS-compatible platforms based on silicon nitride and hydex for nonlinear optics. Nat. Photonics, 7, 597-607(2013).

[96] C. Wang et al. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature, 562, 101-104(2018).