Researching | Advances in High-Dimensional Quantum Key Distribution (Invited)

Acta Optica Sinica, Volume. 45, Issue 13, 1306019(2025)

Advances in High-Dimensional Quantum Key Distribution (Invited)

Fangxiang Wang^1,2, Zhenqiu Zhong^1,2, Shuang Wang^1,2,3、***, Wei Chen^1,2,3、**, and Zhengfu Han^1,2,3、*

Author Affiliations

¹Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, Anhui , China

²Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China, Hefei 230026, Anhui , China

³Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, Anhui , China

show less

Abstract Get PDF(in Chinese)

Figures&Tables (11)

References (101)

Paper Information

References(101)

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

[2] Pirandola S, Andersen U L, Banchi L et al. Advances in quantum cryptography[J]. Advances in Optics and Photonics, 12, 1012(2020).

[3] Xu F H, Ma X F, Zhang Q et al. Secure quantum key distribution with realistic devices[J]. Reviews of Modern Physics, 92, 025002(2020).

[4] Wang S, Chen W, Yin Z Q et al. Field and long-term demonstration of a wide area quantum key distribution network[J]. Optics Express, 22, 21739-21756(2014).

[5] Chen Y A, Zhang Q, Chen T Y et al. An integrated space-to-ground quantum communication network over 4, 600 kilometres[J]. Nature, 589, 214-219(2021).

[6] Li W, Zhang L K, Tan H et al. High-rate quantum key distribution exceeding 110 Mb s-1[J]. Nature Photonics, 17, 416-421(2023).

[7] Grünenfelder F, Boaron A, Resta G V et al. Fast single-photon detectors and real-time key distillation enable high secret-key-rate quantum key distribution systems[J]. Nature Photonics, 17, 422-426(2023).

[8] Bechmann-Pasquinucci H, Peres A. Quantum cryptography with 3-state systems[J]. Physical Review Letters, 85, 3313-3316(2000).

[9] Bechmann-Pasquinucci H, Tittel W. Quantum cryptography using larger alphabets[J]. Physical Review A, 61, 062308(2000).

[10] Bourennane M, Karlsson A, Björk G. Quantum key distribution using multilevel encoding[J]. Physical Review A, 64, 012306(2001).

[11] Cerf N J, Bourennane M, Karlsson A et al. Security of quantum key distribution using d-level systems[J]. Physical Review Letters, 88, 127902(2002).

[12] Cozzolino D, Da Lio B, Bacco D et al. High-dimensional quantum communication: benefits, progress, and future challenges[J]. Advanced Quantum Technologies, 2, 1900038(2019).

[13] Xiong Z X, Shi H D, Wang Y N et al. General quantum key distribution in higher dimension[J]. Physical Review A, 85, 012334(2012).

[14] Bernstein H J. Must quantum theory assume unrestricted superposition?[J]. Journal of Mathematical Physics, 15, 1677-1679(1974).

[15] Ivonovic I D. Geometrical description of quantal state determination[J]. Journal of Physics A: Mathematical and General, 14, 3241(1981).

[16] Wootters W K. Quantum mechanics without probability amplitudes[J]. Foundations of Physics, 16, 391-405(1986).

[17] Gottesman D, Lo H K, Lutkenhaus N et al. Security of quantum key distribution with imperfect devices[C], 136(2005).

[18] Wang X B. Beating the photon-number-splitting attack in practical quantum cryptography[J]. Physical Review Letters, 94, 230503(2005).

[19] Lo H K, Ma X F, Chen K. Decoy state quantum key distribution[J]. Physical Review Letters, 94, 230504(2005).

[20] Lim C C W, Curty M, Walenta N et al. Concise security bounds for practical decoy-state quantum key distribution[J]. Physical Review A, 89, 022307(2014).

[21] Brádler K, Mirhosseini M, Fickler R et al. Finite-key security analysis for multilevel quantum key distribution[J]. New Journal of Physics, 18, 073030(2016).

[22] Zhang Z, Zhao Q, Razavi M et al. Improved key-rate bounds for practical decoy-state quantum-key-distribution systems[J]. Physical Review A, 95, 012333(2017).

[23] Islam N T, Lim C C W, Cahall C et al. Provably secure and high-rate quantum key distribution with time-bin qudits[J]. Science Advances, 3, e1701491(2017).

[24] Wootters W K, Zurek W H. A single quantum cannot be cloned[J]. Nature, 299, 802-803(1982).

[25] Nagali E, Giovannini D, Marrucci L et al. Experimental optimal cloning of four-dimensional quantum states of photons[J]. Physical Review Letters, 105, 073602(2010).

[26] Bouchard F, Fickler R, Boyd R W et al. High-dimensional quantum cloning and applications to quantum hacking[J]. Science Advances, 3, e1601915(2017).

[27] Gisin N, Thew R. Quantum communication[J]. Nature Photonics, 1, 165-171(2007).

[28] Jozsa R, Linden N. On the role of entanglement in quantum-computational speed-up[J]. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 459, 2011-2032(2003).

[29] Degen C L, Reinhard F, Cappellaro P. Quantum sensing[J]. Reviews of Modern Physics, 89, 035002(2017).

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

[31] Kaszlikowski D, Gnacinski P, Zukowski M et al. Violations of local realism by two entangled N-dimensional systems are stronger than for two qubits[J]. Physical Review Letters, 85, 4418-4421(2000).

[32] Durt T, Kaszlikowski D, Żukowski M. Violations of local realism with quantum systems described by N-dimensional Hilbert spaces up to N=16[J]. Physical Review A, 64, 024101(2001).

[33] Gisin N, Ribordy G, Tittel W et al. Quantum cryptography[J]. Reviews of Modern Physics, 74, 145-195(2002).

[34] Yin J, Li Y H, Liao S K et al. Entanglement-based secure quantum cryptography over 1, 120 kilometres[J]. Nature, 582, 501-505(2020).

[35] Doda M, Huber M, Murta G et al. Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement[J]. Physical Review Applied, 15, 034003(2021).

[36] Wengerowsky S, Joshi S K, Steinlechner F et al. An entanglement-based wavelength-multiplexed quantum communication network[J]. Nature, 564, 225-228(2018).

[37] Joshi S K, Aktas D, Wengerowsky S et al. A trusted node-free eight-user metropolitan quantum communication network[J]. Science Advances, 6, eaba0959(2020).

[38] Bennett C H. Quantum cryptography using any two nonorthogonal states[J]. Physical Review Letters, 68, 3121-3124(1992).

[39] Nambu Y, Yoshino K, Tomita A. Quantum encoder and decoder for practical quantum key distribution using a planar lightwave circuit[J]. Journal of Modern Optics, 55, 1953-1970(2008).

[40] Ali-Khan I, Broadbent C J, Howell J C. Large-alphabet quantum key distribution using energy-time entangled bipartite states[J]. Physical Review Letters, 98, 060503(2007).

[41] Mower J, Zhang Z S, Desjardins P et al. High-dimensional quantum key distribution using dispersive optics[J]. Physical Review A, 87, 062322(2013).

[42] Zhang Z S, Mower J, Englund D et al. Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry[J]. Physical Review Letters, 112, 120506(2014).

[43] Islam N T, Lim C C W, Cahall C et al. Scalable high-rate, high-dimensional time-bin encoding quantum key distribution[J]. Quantum Science and Technology, 4, 035008(2019).

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

[45] Mirhosseini M, Magaña-Loaiza O S, O’Sullivan M N et al. High-dimensional quantum cryptography with twisted light[J]. New Journal of Physics, 17, 033033(2015).

[46] Zhou Y Y, Mirhosseini M, Oliver S et al. Using all transverse degrees of freedom in quantum communications based on a generic mode sorter[J]. Optics Express, 27, 10383-10394(2019).

[47] Otte E, Nape I, Rosales-Guzmán C et al. High-dimensional cryptography with spatial modes of light: tutorial[J]. Journal of the Optical Society of America B, 37, A309-A323(2020).

[48] Sit A, Bouchard F, Fickler R et al. High-dimensional intracity quantum cryptography with structured photons[J]. Optica, 4, 1006-1010(2017).

[49] Cozzolino D, Bacco D, Da Lio B et al. Orbital angular momentum states enabling fiber-based high-dimensional quantum communication[J]. Physical Review Applied, 11, 064058(2019).

[50] Wang Q K, Wang F X, Liu J et al. High-dimensional quantum cryptography with hybrid orbital-angular-momentum states through 25 km of ring-core fiber: a proof-of-concept demonstration[J]. Physical Review Applied, 15, 064034(2021).

[51] Ramachandran S, Kristensen P, Yan M F. Generation and propagation of radially polarized beams in optical fibers[J]. Optics Letters, 34, 2525-2527(2009).

[52] Gregg P, Kristensen P, Golowich S E et al. Stable transmission of 12 OAM states in air-core fiber[C], CTu2K.2-14(2013).

[53] Willner A E, Huang H, Yan Y et al. Optical communications using orbital angular momentum beams[J]. Advances in Optics and Photonics, 7, 66-106(2015).

[54] Cañas G, Vera N, Cariñe J et al. High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers[J]. Physical Review A, 96, 022317(2017).

[55] Ding Y H, Bacco D, Dalgaard K et al. High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits[J]. NPJ Quantum Information, 3, 25(2017).

[56] Lee H J, Choi S K, Park H S. Experimental demonstration of four-dimensional photonic spatial entanglement between multi-core optical fibres[J]. Scientific Reports, 7, 4302(2017).

[57] Lee H J, Park H S. Generation and measurement of arbitrary four-dimensional spatial entanglement between photons in multicore fibers[J]. Photonics Research, 7, 19-27(2019).

[58] Hu X M, Xing W B, Liu B H et al. Efficient distribution of high-dimensional entanglement through 11 km fiber[J]. Optica, 7, 738-743(2020).

[59] Hu X M, Huang C X, Sheng Y B et al. Long-distance entanglement purification for quantum communication[J]. Physical Review Letters, 126, 010503(2021).

[60] Zahidy M, Ribezzo D, De Lazzari C et al. Practical high-dimensional quantum key distribution protocol over deployed multicore fiber[J]. Nature Communications, 15, 1651(2024).

[61] Mao Q P, Wang L, Zhao S M. Efficient quantum key distribution based on hybrid degrees of freedom[J]. Laser Physics, 29, 085201(2019).

[62] Wang J D, Wei Z J, Zhang H et al. Efficient quantum key distribution via single-photon two-qubit states[J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 43, 095504(2010).

[63] Erhard M, Qassim H, Mand H et al. Real-time imaging of spin-to-orbital angular momentum hybrid remote state preparation[J]. Physical Review A, 92, 022321(2015).

[64] Wang F X, Chen W, Yin Z Q et al. Characterizing high-quality high-dimensional quantum key distribution by state mapping between different degrees of freedom[J]. Physical Review Applied, 11, 024070(2019).

[65] Wang F X, Lu Q H, Chen W et al. Hybrid high-dimensional quantum key distribution for a composable quantum network[J]. Physical Review Applied, 19, 054060(2023).

[66] 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).

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

[68] Krenn M, Handsteiner J, Fink M et al. Twisted photon entanglement through turbulent air across Vienna[J]. Proceedings of the National Academy of Sciences of the United States of America, 112, 14197-14201(2015).

[69] Cao H, Gao S C, Zhang C et al. Distribution of high-dimensional orbital angular momentum entanglement over a 1 km few-mode fiber[J]. Optica, 7, 232-237(2020).

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

[71] 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).

[72] Fontaine N K, Ryf R, Chen H S et al. Laguerre-Gaussian mode sorter[J]. Nature Communications, 10, 1865(2019).

[73] Reck M, Zeilinger A, Bernstein H J et al. Experimental realization of any discrete unitary operator[J]. Physical Review Letters, 73, 58-61(1994).

[74] 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).

[75] Xavier G B, Lima G. Quantum information processing with space-division multiplexing optical fibres[J]. Communications Physics, 3, 9(2020).

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

[77] Bulla L, Hjorth K, Kohout O et al. Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere[J]. Physical Review A, 107, L050402(2023).

[78] Ikuta T, Takesue H. Four-dimensional entanglement distribution over 100 km[J]. Scientific Reports, 8, 817(2018).

[79] Liu J Y, Lin Z H, Liu D N et al. High-dimensional quantum key distribution using energy-time entanglement over 242 km partially deployed fiber[J]. Quantum Science and Technology, 9, 015003(2024).

[80] Yu H, Sciara S, Chemnitz M et al. Quantum key distribution implemented with d-level time-bin entangled photons[J]. Nature Communications, 16, 171(2025).

[81] Nunn J, Wright L J, Söller C et al. Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion[J]. Optics Express, 21, 15959-15973(2013).

[82] Bouchard F, Bonsma-Fisher K, Heshami K et al. Measuring ultrafast time-bin qudits[J]. Physical Review A, 107, 022618(2023).

[83] Ramelow S, Ratschbacher L, Fedrizzi A et al. Discrete tunable color entanglement[J]. Physical Review Letters, 103, 253601(2009).

[84] Kues M, Reimer C, Lukens J M et al. Quantum optical microcombs[J]. Nature Photonics, 13, 170-179(2019).

[85] Chapman J C, Lim C C W, Kwiat P G. Hyperentangled time-bin and polarization quantum key distribution[J]. Physical Review Applied, 18, 044027(2022).

[86] Zhong Z Q, Zhan X H, Chen J L et al. Hyperentanglement quantum communication over a 50 km noisy fiber channel[J]. Optica, 11, 1056-1061(2024).

[87] Cozzolino D, Polino E, Valeri M et al. Air-core fiber distribution of hybrid vector vortex-polarization entangled states[J]. Advanced Photonics, 1, 046005(2019).

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

[89] Bennett C H, Brassard G, Popescu S et al. Purification of noisy entanglement and faithful teleportation via noisy channels[J]. Physical Review Letters, 76, 722-725(1996).

[90] Reichle R, Leibfried D, Knill E et al. Experimental purification of two-atom entanglement[J]. Nature, 443, 838-841(2006).

[91] Kalb N, Reiserer A A, Humphreys P C et al. Entanglement distillation between solid-state quantum network nodes[J]. Science, 356, 928-932(2017).

[92] Stephenson L J, Nadlinger D P, Nichol B C et al. High-rate, high-fidelity entanglement of qubits across an elementary quantum network[J]. Physical Review Letters, 124, 110501(2020).

[93] Pan J W, Gasparoni S, Ursin R et al. Experimental entanglement purification of arbitrary unknown states[J]. Nature, 423, 417-422(2003).

[94] Yamamoto T, Koashi M, Özdemir Ş K et al. Experimental extraction of an entangled photon pair from two identically decohered pairs[J]. Nature, 421, 343-346(2003).

[95] Knill E, Laflamme R, Milburn G J. A scheme for efficient quantum computation with linear optics[J]. Nature, 409, 46-52(2001).

[96] Ecker S, Sohr P, Bulla L et al. Experimental single-copy entanglement distillation[J]. Physical Review Letters, 127, 040506(2021).

[97] Fiorentino M, Wong F N C. Deterministic controlled-NOT gate for single-photon two-qubit quantum logic[J]. Physical Review Letters, 93, 070502(2004).

[98] 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).

[99] Bütow J, Eismann J S, Sharma V et al. Generating free-space structured light with programmable integrated photonics[J]. Nature Photonics, 18, 243-249(2024).

[100] SeyedinNavadeh S, Milanizadeh M, Zanetto F et al. Determining the optimal communication channels of arbitrary optical systems using integrated photonic processors[J]. Nature Photonics, 18, 149-155(2023).

[101] Wang S, Yin Z Q, He D Y et al. Twin-field quantum key distribution over 830-km fibre[J]. Nature Photonics, 16, 154-161(2022).

Tools

Get Citation

Copy Citation Text

Fangxiang Wang, Zhenqiu Zhong, Shuang Wang, Wei Chen, Zhengfu Han. Advances in High-Dimensional Quantum Key Distribution (Invited)[J]. Acta Optica Sinica, 2025, 45(13): 1306019

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Fiber Optics and Optical Communications

Received: May. 22, 2025

Accepted: Jun. 30, 2025

Published Online: Jul. 18, 2025

The Author Email: Shuang Wang (wshuang@ustc.edu.cn), Wei Chen (weich@ustc.edu.cn), Zhengfu Han (zfhan@ustc.edu.cn)

DOI:10.3788/AOS251137

CSTR:32393.14.AOS251137

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology