[1] Bennett C H, Brassard G. Quantum cryptography: public key distribution and coin tossing[J]. Theoretical Computer Science, 560, 7-11(2014).

[2] Mattle K, Weinfurter H, Kwiat P G et al. Dense coding in experimental quantum communication[J]. Physical Review Letters, 76, 4656-4659(1996).

[3] Bouwmeester D, Pan J W, Mattle K et al. Experimental quantum teleportation[J]. Nature, 390, 575-579(1997).

[4] Pan J W, Bouwmeester D, Weinfurter H et al. Experimental entanglement swapping: entangling photons that never interacted[J]. Physical Review Letters, 80, 3891-3894(1998).

[5] Bouwmeester D, Pan J W, Daniell M et al. Observation of three-photon Greenberger-Horne-Zeilinger entanglement[J]. Physical Review Letters, 82, 1345-1349(1999).

[6] Yin J, Cao Y, Li Y H et al. Satellite-based entanglement distribution over 1200 kilometers[J]. Science, 356, 1140-1144(2017).

[7] Liao S K, Cai W Q, Liu W Y et al. Satellite-to-ground quantum key distribution[J]. Nature, 549, 43-47(2017).

[8] Ren J G, Xu P, Yong H L et al. Ground-to-satellite quantum teleportation[J]. Nature, 549, 70-73(2017).

[9] Pan J W, Daniell M, Gasparoni S et al. Experimental demonstration of four-photon entanglement and high-fidelity teleportation[J]. Physical Review Letters, 86, 4435-4438(2001).

[10] Zhao Z, Chen Y A, Zhang A N et al. Experimental demonstration of five-photon entanglement and open-destination teleportation[J]. Nature, 430, 54-58(2004).

[11] Lu C Y, Zhou X Q, Gühne O et al. Experimental entanglement of six photons in graph states[J]. Nature Physics, 3, 91-95(2007).

[12] Yao X C, Wang T X, Xu P et al. Observation of eight-photon entanglement[J]. Nature Photonics, 6, 225-228(2012).

[13] Huang Y F, Liu B H, Peng L et al. Experimental generation of an eight-photon Greenberger-Horne-Zeilinger state[J]. Nature Communications, 2, 546(2011).

[14] Wang X L, Chen L K, Li W et al. Experimental ten-photon entanglement[J]. Physical Review Letters, 117, 210502(2016).

[15] Chen L K, Li Z D, Yao X C et al. Observation of ten-photon entanglement using thin BiB3O6 crystals[J]. Optica, 4, 77-83(2017).

[16] Zhong H S, Li Y, Li W et al. 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion[J]. Physical Review Letters, 121, 250505(2018).

[17] Wang J W, Paesani S, Ding Y H et al. Multidimensional quantum entanglement with large-scale integrated optics[J]. Science, 360, 285-291(2018).

[18] Hu X M, Xing W B, Liu B H et al. Efficient generation of high-dimensional entanglement through multipath down-conversion[J]. Physical Review Letters, 125, 090503(2020).

[19] Li L, Liu Z X, Ren X F et al. Metalens-array-based high-dimensional and multiphoton quantum source[J]. Science, 368, 1487-1490(2020).

[20] Martin A, Guerreiro T, Tiranov A et al. Quantifying photonic high-dimensional entanglement[J]. Physical Review Letters, 118, 110501(2017).

[21] Xie Z D, Zhong T, Shrestha S et al. Harnessing high-dimensional hyperentanglement through a biphoton frequency comb[J]. Nature Photonics, 9, 536-542(2015).

[22] Reimer C, Kues M, Roztocki P et al. Generation of multiphoton entangled quantum states by means of integrated frequency combs[J]. Science, 351, 1176-1180(2016).

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

[24] Allen L, Beijersbergen M W. Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 45, 8185-8189(1992).

[25] Padgett M J. Orbital angular momentum 25 years on[J]. Optics Express, 25, 11265-11274(2017).

[26] Shen Y J, Wang X J, Xie Z W et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities[J]. Light: Science & Applications, 8, 90(2019).

[27] Erhard M, Fickler R, Krenn M et al. Twisted photons: new quantum perspectives in high dimensions[J]. Light: Science & Applications, 7, 17146(2018).

[28] Erhard M, Krenn M, Zeilinger A. Advances in high-dimensional quantum entanglement[J]. Nature Reviews Physics, 2, 365-381(2020).

[29] Fickler R, Lapkiewicz R, Plick W N et al. Quantum entanglement of high angular momenta[J]. Science, 338, 640-643(2012).

[30] Fickler R, Campbell G, Buchler B et al. Quantum entanglement of angular momentum states with quantum numbers up to 10, 010[J]. Proceedings of the National Academy of Sciences of the United States of America, 113, 13642-13647(2016).

[31] Krenn M, Huber M, Fickler R et al. Generation and confirmation of a (100 × 100)-dimensional entangled quantum system[J]. Proceedings of the National Academy of Sciences of the United States of America, 111, 6243-6247(2014).

[32] Kotlyar V V, Almazov A A, Khonina S N et al. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate[J]. Journal of the Optical Society of America A, 22, 849-861(2005).

[33] Curtis J E, Grier D G. Structure of optical vortices[J]. Physical Review Letters, 90, 133901(2003).

[34] Marrucci L, Manzo C, Paparo D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media[J]. Physical Review Letters, 96, 163905(2006).

[35] Leach J, Padgett M J, Barnett S M et al. Measuring the orbital angular momentum of a single photon[J]. Physical Review Letters, 88, 257901(2002).

[36] Nagali E, Sansoni L, Sciarrino F et al. Optimal quantum cloning of orbital angular momentum photon qubits through Hong-Ou-Mandel coalescence[J]. Nature Photonics, 3, 720-723(2009).

[37] Wang X L, Cai X D, Su Z E et al. Quantum teleportation of multiple degrees of freedom of a single photon[J]. Nature, 518, 516-519(2015).

[38] Slussarenko S. D’Ambrosio V, Piccirillo B, et al. The polarizing Sagnac interferometer: a tool for light orbital angular momentum sorting and spin-orbit photon processing[J]. Optics Express, 18, 27205-27216(2010).

[39] Zhang W H, Qi Q Q, Zhou J et al. Mimicking faraday rotation to sort the orbital angular momentum of light[J]. Physical Review Letters, 112, 153601(2014).

[40] Courtial J, Robertson D A, Dholakia K et al. Rotational frequency shift of a light beam[J]. Physical Review Letters, 81, 4828-4830(1998).

[41] Li S M, Qian S X, Kong L J et al. An efficient and robust scheme for controlling the states of polarization in a Sagnac interferometric configuration[J]. EPL, 105, 64006(2014).

[42] Wang X L, Luo Y H, Huang H L et al. 18-qubit entanglement with six photons’ three degrees of freedom[J]. Physical Review Letters, 120, 260502(2018).

[43] Nagali E. Sciarrino F, de Martini F, et al. Quantum information transfer from spin to orbital angular momentum of photons[J]. Physical Review Letters, 103, 013601(2009).

[44] D’Ambrosio V, Nagali E, Monken C H et al. Deterministic qubit transfer between orbital and spin angular momentum of single photons[J]. Optics Letters, 37, 172-174(2012).

[45] D’Ambrosio V, Spagnolo N, del Re L et al. Photonic polarization gears for ultra-sensitive angular measurements[J]. Nature Communications, 4, 2432(2013).

[46] Wang X L, Ding J P, Ni W J et al. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement[J]. Optics Letters, 32, 3549-3551(2007).

[47] Maurer C, Jesacher A, Fürhapter S et al. Tailoring of arbitrary optical vector beams[J]. New Journal of Physics, 9, 78(2007).

[48] Jones P H, Rashid M, Makita M et al. Sagnac interferometer method for synthesis of fractional polarization vortices[J]. Optics Letters, 34, 2560-2562(2009).

[49] Liu S, Qi S X, Zhang Y et al. Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude[J]. Photonics Research, 6, 228-233(2018).

[50] Gao Y, Chen Z Z, Ding J P et al. Single ultra-high-definition spatial light modulator enabling highly efficient generation of fully structured vector beams[J]. Applied Optics, 58, 6591-6596(2019).

[51] Wang J, Yang J Y, Fazal I M et al. Terabit free-space data transmission employing orbital angular momentum multiplexing[J]. Nature Photonics, 6, 488-496(2012).

[52] Zhu L, Wang J. Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element[J]. Optics Express, 23, 26221-26233(2015).

[53] Wan C H, Chen J, Zhan Q W. Tailoring optical orbital angular momentum spectrum with spiral complex field modulation[J]. Optics Express, 25, 15108-15117(2017).

[54] Kitagawa T, Rudner M S, Berg E et al. Exploring topological phases with quantum walks[J]. Physical Review A, 82, 033429(2010).

[55] Hasan M Z, Kane C L. Colloquium: topological insulators[J]. Reviews of Modern Physics, 82, 3045-3067(2010).

[56] Goyal S K, Roux F S, Forbes A et al. Implementing quantum walks using orbital angular momentum of classical light[J]. Physical Review Letters, 110, 263602(2013).

[57] Cardano F, Massa F, Qassim H et al. Quantum walks and wavepacket dynamics on a lattice with twisted photons[J]. Science Advances, 1, e1500087(2015).

[58] Wang B, Chen T, Zhang X D. Experimental observation of topologically protected bound states with vanishing Chern numbers in a two-dimensional quantum walk[J]. Physical Review Letters, 121, 100501(2018).

[59] Yuan L Q, Lin Q, Zhang A W et al. Photonic gauge potential in one cavity with synthetic frequency and orbital angular momentum dimensions[J]. Physical Review Letters, 122, 083903(2019).

[60] Wehner S, Elkouss D. 362(6412): eaam9288[J]. Hanson R. Quantum internet: a vision for the road ahead. Science(2018).

[61] Yu Y, Ma F, Luo X Y et al. Entanglement of two quantum memories via fibres over dozens of kilometres[J]. Nature, 578, 240-245(2020).

[62] Zhou Z Y, Li Y, Ding D S et al. Orbital angular momentum photonic quantum interface[J]. Light: Science & Applications, 5, e16019(2016).

[63] Zhou Z Y, Liu S L, Li Y et al. Orbital angular momentum-entanglement frequency transducer[J]. Physical Review Letters, 117, 103601(2016).

[64] Liu S L, Yang C, Xu Z H et al. High-dimensional quantum frequency converter[J]. Physical Review A, 101, 012339(2020).

[65] Wu H J, Zhao B, Rosales-Guzmán C et al. Spatial-polarization-independent parametric up-conversion of vectorially structured light[J]. Physical Review Applied, 13, 064041(2020).

[66] Ren Z C, Lou Y C, Cheng Z M et al. Optical frequency conversion of light with maintaining polarization and orbital angular momentum[J]. Optics Letters, 46, 2300-2303(2021).

[67] Bozinovic N, Yue Y, Ren Y X et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers[J]. Science, 340, 1545-1548(2013).

[68] Gregg P, Kristensen P, Ramachandran S. Conservation of orbital angular momentum in air-core optical fibers[J]. Optica, 2, 267-270(2015).

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

[70] Barreiro J T, Langford N K, Peters N A et al. Generation of hyperentangled photon pairs[J]. Physical Review Letters, 95, 260501(2005).

[71] Yang T, Zhang Q, Zhang J et al. All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement[J]. Physical Review Letters, 95, 240406(2005).

[72] Cinelli C, Barbieri M, Perris R et al. All-versus-nothing nonlocality test of quantum mechanics by two-photon hyperentanglement[J]. Physical Review Letters, 95, 240405(2005).

[73] Barbieri M, de Martini F, Mataloni P et al. Enhancing the violation of the Einstein-Podolsky-Rosen local realism by quantum hyperentanglement[J]. Physical Review Letters, 97, 140407(2006).

[74] Chen K, Li C M, Zhang Q et al. Experimental realization of one-way quantum computing with two-photon four-qubit cluster states[J]. Physical Review Letters, 99, 120503(2007).

[75] Schuck C, Huber G, Kurtsiefer C et al. Complete deterministic linear optics Bell state analysis[J]. Physical Review Letters, 96, 190501(2006).

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

[77] Williams B P, Sadlier R J, Humble T S. Superdense coding over optical fiber links with complete bell-state measurements[J]. Physical Review Letters, 118, 050501(2017).

[78] Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states[J]. Physical Review Letters, 69, 2881-2884(1992).

[79] Bennett C H, Brassard G, Crépeau C et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Physical Review Letters, 70, 1895-1899(1993).

[80] Wei T C, Barreiro J T, Kwiat P G. Hyperentangled Bell-state analysis[J]. Physical Review A, 75, 060305(2007).

[81] Hu X M, Guo Y, Liu B H et al. 4(7): eaat9304(2018).

[82] Kong L J, Liu R, Qi W R et al. 5(6): eaat9206(2019).

[83] di Lorenzo Pires H, Florijn H C B, van Exter M P. Measurement of the spiral spectrum of entangled two-photon states[J]. Physical Review Letters, 104, 020505(2010).

[84] Dada A C, Leach J, Buller G S et al. Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities[J]. Nature Physics, 7, 677-680(2011).

[85] Torres J P, Alexandrescu A, Torner L. Quantum spiral bandwidth of entangled two-photon states[J]. Physical Review A, 68, 050301(2003).

[86] Liu S L, Zhou Z Y, Liu S K et al. Coherent manipulation of a three-dimensional maximally entangled state[J]. Physical Review A, 98, 062316(2018).

[87] Wang F R, Erhard M, Babazadeh A et al. Generation of the complete four-dimensional Bell basis[J]. Optica, 4, 1462-1467(2017).

[88] Chen Y Y, Zhang W H, Zhang D K et al. Coherent generation of the complete high-dimensional bell basis by adaptive pump modulation[J]. Physical Review Applied, 14, 054069(2020).

[89] Liu S L, Zhang Y W, Yang C et al. Increasing two-photon entangled dimensions by shaping input-beam profiles[J]. Physical Review A, 101, 052324(2020).

[90] Kovlakov E V, Straupe S S, Kulik S P. Quantum state engineering with twisted photons via adaptive shaping of the pump beam[J]. Physical Review A, 98, 060301(2018).

[91] Krenn M, Hochrainer A, Lahiri M et al. Entanglement by path identity[J]. Physical Review Letters, 118, 080401(2017).

[92] Kysela J, Erhard M, Hochrainer A et al. Path identity as a source of high-dimensional entanglement[J]. Proceedings of the National Academy of Sciences of the United States of America, 117, 26118-26122(2020).

[93] Zhang W H, Qi Q Q, Zhou J et al. Mimicking faraday rotation to sort the orbital angular momentum of light[J]. Physical Review Letters, 112, 153601(2014).

[94] Berkhout G C G, Lavery M P J, Courtial J et al. Efficient sorting of orbital angular momentum states of light[J]. Physical Review Letters, 105, 153601(2010).

[95] Mirhosseini M, Malik M, Shi Z M et al. Efficient separation of the orbital angular momentum eigenstates of light[J]. Nature Communications, 4, 2781(2013).

[96] Wen Y H, Chremmos I, Chen Y J et al. Spiral transformation for high-resolution and efficient sorting of optical vortex modes[J]. Physical Review Letters, 120, 193904(2018).

[97] Wan C H, Chen J, Zhan Q W. Compact and high-resolution optical orbital angular momentum sorter[J]. APL Photonics, 2, 031302(2017).

[98] Ruffato G, Massari M, Romanato F. Compact sorting of optical vortices by means of diffractive transformation optics[J]. Optics Letters, 42, 551-554(2017).

[99] Wen Y H, Chremmos I, Chen Y J et al. Compact and high-performance vortex mode sorter for multi-dimensional multiplexed fiber communication systems[J]. Optica, 7, 254-262(2020).

[100] Fickler R, Lapkiewicz R, Huber M et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information[J]. Nature Communications, 5, 4502(2014).

[101] Howell J C, Bennink R S, Bentley S J et al. Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion[J]. Physical Review Letters, 92, 210403(2004).

[102] Leach J, Jack B, Romero J et al. Quantum correlations in optical angle-orbital angular momentum variables[J]. Science, 329, 662-665(2010).

[103] Chen L X, Ma T L, Qiu X D et al. Realization of the Einstein-Podolsky-Rosen paradox using radial position and radial momentum variables[J]. Physical Review Letters, 123, 060403(2019).

[104] Kulkarni G, Sahu R. Magaña-Loaiza O S, et al. Single-shot measurement of the orbital-angular-momentum spectrum of light[J]. Nature Communications, 8, 1054(2017).

[105] Kong L J, Liu R, Qi W R et al. Asymptotical locking tomography of high-dimensional entanglement[J]. Chinese Physics Letters, 37, 034204(2020).

[106] Hiesmayr B C, Löffler W. Observation of four-photon orbital angular momentum entanglement[J]. Physical Review Letters, 116, 073601(2016).

[107] Malik M, Erhard M, Huber M et al. Multi-photon entanglement in high dimensions[J]. Nature Photonics, 10, 248-252(2016).

[108] Erhard M, Malik M, Krenn M et al. Experimental Greenberger-Horne-Zeilinger entanglement beyond qubits[J]. Nature Photonics, 12, 759-764(2018).

[109] Luo Y H, Chen M C, Erhard M et al. Quantum teleportation of physical qubits into logical code spaces[J]. Proceedings of the National Academy of Sciences of the United States of America, 118, e2026250118(2021).

[110] Vitelli C, Spagnolo N, Aparo L et al. Joining the quantum state of two photons into one[J]. Nature Photonics, 7, 521-526(2013).

[111] Neergaard-Nielsen J S. Two become one[J]. Nature Photonics, 7, 512-513(2013).

[112] Zhong H S, Wang H, Deng Y H et al. Quantum computational advantage using photons[J]. Science, 370, 1460-1463(2020).

[113] Zhong H S, Deng Y H, Qin J et al. Phase-programmable gaussian boson sampling using stimulated squeezed light[J]. Physical Review Letters, 127, 180502(2021).

[114] Weinfurter H. ukowski M. Four-photon entanglement from down-conversion[J]. Physical Review A, 64, 010102(2001).

[115] Gao X Q, Krenn M, Kysela J et al. Arbitrary d-dimensional Pauli X gates of a flying qudit[J]. Physical Review A, 99, 023825(2019).

[116] Babazadeh A, Erhard M, Wang F R et al. High-dimensional single-photon quantum gates: concepts and experiments[J]. Physical Review Letters, 119, 180510(2017).

[117] Asadian A, Erker P, Huber M et al. Heisenberg-Weyl observables: Bloch vectors in phase space[J]. Physical Review A, 94, 010301(2016).

[118] Wang Y C, Hu Z X, Sanders B C et al. Qudits and high-dimensional quantum computing[J]. Frontiers in Physics, 8, 589504(2020).

[119] Gao X Q, Erhard M, Zeilinger A et al. Computer-inspired concept for high-dimensional multipartite quantum gates[J]. Physical Review Letters, 125, 050501(2020).