Measurement-device-independent quantum key distribution with entanglement-assisted linear Bell state measurement

doi:10.1088/1674-1056/ae3605

中国物理B ›› 2026, Vol. 35 ›› Issue (4): 40310-040310.doi: 10.1088/1674-1056/ae3605

所属专题： SPECIAL TOPIC — Quantum communication and quantum network

Measurement-device-independent quantum key distribution with entanglement-assisted linear Bell state measurement

Cheng Zhang(张诚)¹, Cheng Liu(刘成)², Jiawei Ying(应佳伟)¹, Shipu Gu(顾世浦)¹, Lan Zhou(周澜)², Yin Ma(马寅)^3,†, Kang Gao(高亢)⁴, Hai Wei(魏海)^3,4, Kai Wen(文凯)^3,4, and Yubo Sheng(盛宇波)^1,‡

1 College of Electronic and Optical Engineering, College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
3 Beijing QBoson Quantum Technology Co. Ltd., Beijing 100015, China;
4 Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China

收稿日期:2025-10-22 修回日期:2026-01-06 接受日期:2026-01-09 出版日期:2026-03-24 发布日期:2026-03-24
通讯作者: Yin Ma, Yubo Sheng E-mail:may@boseq.com;shengyb@njupt.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12574393, 12175106, and 92365110), the Research Initiation Fund of the Quantum Science Center of the Guangdong–Hong Kong–Macao Greater Bay Area (Grant No. QD2305001), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX23-0989).

Measurement-device-independent quantum key distribution with entanglement-assisted linear Bell state measurement

1 College of Electronic and Optical Engineering, College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
3 Beijing QBoson Quantum Technology Co. Ltd., Beijing 100015, China;
4 Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China

Received:2025-10-22 Revised:2026-01-06 Accepted:2026-01-09 Online:2026-03-24 Published:2026-03-24
Contact: Yin Ma, Yubo Sheng E-mail:may@boseq.com;shengyb@njupt.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12574393, 12175106, and 92365110), the Research Initiation Fund of the Quantum Science Center of the Guangdong–Hong Kong–Macao Greater Bay Area (Grant No. QD2305001), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX23-0989).

摘要/Abstract

摘要： Measurement-device-independent quantum key distribution (MDI QKD) provides inherent immunity against attacks targeting practical measurement devices. Existing MDI QKD protocols all rely on Bell-state measurements (BSM) to establish correlations between the users. However, the success probability of linear-optics BSM is limited to 50%, which severely restricts the achievable key rate of MDI QKD. We propose a high-capacity MDI QKD protocol with entanglement-assisted linear-optical BSM. This protocol has three advantages. First, compared with the original MDI QKD, at least a 25% increase in the key rate can be achieved. Second, simulation results show that this protocol can effectively increase the maximum photon transmission distance of MDI QKD from 262 km to 272 km. Third, this protocol is feasible in a fully linear-optical system under current experimental conditions. Our protocol provides a potential approach for improving the performance of future quantum communication networks.

关键词: measurement-device-independent quantum key distribution, linear-optical Bell state measurement, entanglement assistance

Abstract: Measurement-device-independent quantum key distribution (MDI QKD) provides inherent immunity against attacks targeting practical measurement devices. Existing MDI QKD protocols all rely on Bell-state measurements (BSM) to establish correlations between the users. However, the success probability of linear-optics BSM is limited to 50%, which severely restricts the achievable key rate of MDI QKD. We propose a high-capacity MDI QKD protocol with entanglement-assisted linear-optical BSM. This protocol has three advantages. First, compared with the original MDI QKD, at least a 25% increase in the key rate can be achieved. Second, simulation results show that this protocol can effectively increase the maximum photon transmission distance of MDI QKD from 262 km to 272 km. Third, this protocol is feasible in a fully linear-optical system under current experimental conditions. Our protocol provides a potential approach for improving the performance of future quantum communication networks.

Key words: measurement-device-independent quantum key distribution, linear-optical Bell state measurement, entanglement assistance

中图分类号: (Quantum information)

03.67.-a

03.67.Ac (Quantum algorithms, protocols, and simulations) 03.67.Hk (Quantum communication) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)

Cheng Zhang(张诚), Cheng Liu(刘成), Jiawei Ying(应佳伟), Shipu Gu(顾世浦), Lan Zhou(周澜), Yin Ma(马寅), Kang Gao(高亢), Hai Wei(魏海), Kai Wen(文凯), and Yubo Sheng(盛宇波). Measurement-device-independent quantum key distribution with entanglement-assisted linear Bell state measurement[J]. 中国物理B, 2026, 35(4): 40310-040310.

参考文献

[1] Bennett C H and DiVincenzo D P 2000 Nature 404 247
[2] Degen C L, Reinhard F and Cappellaro P 2017 Rev. Mod. Phys. 89 035002
[3] Gisin N and Thew R 2007 Nat. Photonics 1 165
[4] Bennett C H and Brassard G 1984 Proc. IEEE Int. Conf. Comput. Syst. Signal Process, Bangalore, India, pp. 175
[5] Ekert A K 1991 Phys. Rev. Lett. 67 661
[6] Bennett C H 1992 Phys. Rev. Lett. 68 3121
[7] Scarani V, Acín A, Ribordy G and Gisin N 2004 Phys. Rev. Lett. 92 057901
[8] Zhao Y, Qi B, Ma X F, Lo H K and Qian L 2006 Phys. Rev. Lett. 96 070502
[9] Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P and Diamanti E 2013 Nat. Photonics 7 378
[10] Ma X F, Zeng P and Zhou H 2018 Phys. Rev. X 8 031043
[11] Wang S, Yin Z Q, He D Y, ChenW,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 and Han Z F 2022 Nat. Photonics 16 154
[12] Huang C F, Chen Y, Jin L, Chen Y, Geng M, Wang J, Zhang Z and Wei K 2022 Phys. Rev. A 105 012421
[13] Lin X,Wang R,Wang S, Yin Z Q, ChenW, Guo G C and Han Z F 2022 Phys. Rev. Lett. 129 050506
[14] 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 and Pan J W 2023 Nat. Photonics 17 416
[15] Wei K J, Hu X, Du Y Q, Hua X, Zhao Z, Chen Y, Huang C F and Xiao X 2023 Photon. Res. 11 1364
[16] Huang A Q, Mizutani A, Lo H K, Makarov V and Tamaki K 2023 Phys. Rev. Appl. 19 014048
[17] Feng B, Huang H D, Bian Y X, Jia W, Zhou X Y and Wang Q 2023 Chin. Phys. B 32 030307
[18] Zhou C,Wang H T, Lu Y F, Jiang X L, Zhao Y M, Zhou Y,Wang Y, Li J J, Zhou Y Y, Wang X, Li H W and Bao W S 2024 Chin. Phys. B 33 100302
[19] Zhang C X, Li J G,Wang Y, ChenW, Zhang J S and An J M 2025 Chin. Phys. B 34 050303
[20] Liu C, Li Y, Wang H Y, Shi K Y, Ma D, Zhang Y J and Ma H Q 2025 Chin. Phys. Lett. 42 010301
[21] Xu H X, Wang S H, Wang C L and Zhang P 2025 Chin. Phys. Lett. 42 010303
[22] Li Y, Cai W Q, Ren J G, et al. 2025 Nature 640 47
[23] Daniil Trefilov, Xoel Sixto, Víctor Zapatero, Anqi Huang, Marcos Curty, Vadim Makarov 2025 Optica Quantum 3 417
[24] Chen Y, Huang C F, Lin G S, Huang S, Zhang Z R and Wei K J 2025 J. Lightwave Technol. 43 5032
[25] Niu P H, Zhou Z R, Lin Z S, Sheng Y B, Yin L G and Long G L 2018 Sci. Bull. 63 1345
[26] Zhou Z R, Sheng Y B, Niu P H, Yin L G, Long G L and Hanzo L 2020 Sci. China Phys. Mech. Astron. 63 230362
[27] Ying J W, Zhou L, Zhong W and Sheng Y B 2022 Chin. Phys. B 31 120303
[28] Pan D, Long G L, Yin L G, Sheng Y B, Ruan D, Ng S X, Lu J H and Hanzo L 2024 IEEE Commun. Surv. Tutor. 26 1898
[29] Shukla C, Shukla A, Chatzinotas S and Nesladek M 2025 AAPPS Bull. 35 20
[30] Fu Y, Yin H L, Chen T Y and Chen Z B 2015 Phys. Rev. Lett. 114 090501
[31] Ju X X, Zhong W, Sheng Y B and Zhou L 2023 Chin. Phys. B 31 100302
[32] Liu T G, Lai J C, Li Z H and Li T 2025 Phys. Rev. Appl. 23 034057
[33] Zhang Q, Ying J W, Wang Z J, Zhong W, Du M M, Shen S T, Li X Y, Zhang A L, Gu S P,Wang X F, Zhou L and Sheng Y B 2025 Phys. Rev. A 111 012603
[34] Lu Y S, Yin H L, Xie Y M, Fu Y and Chen Z B 2025 Rep. Prog. Phys. 88 067901
[35] Yin H L, Fu Y, Li C L, Weng C X, Li B H, Gu J, Lu Y S, Huang S and Chen Z B 2022 Natl. Sci. Rev. 10 nwac228
[36] Du Y, Li B H, Hua X, Cao X Y, Zhao Z, Xie F, Zhang Z, Yin H L, Xiao X and Wei K 2025 Light Sci. Appl. 14 108
[37] Wang X B 2005 Phys. Rev. Lett. 94 230503
[38] Ashkenazy A, Idan Y, Korn D, Fixler D, Dayan B and Cohen E 2024 Adv. Quantum Technol. 7 2300437
[39] Gisin N, Fasel S, Kraus B, Zbinden H and Ribordy G 2006 Phys. Rev. A 73 022320
[40] Jain N, Anisimova E, Khan I, Makarov V, Marquardt C and Leuchs G 2014 New J. Phys. 16 123030
[41] Qi B, Fung C H F, Lo H K and Ma X F 2007 Quant. Inf. Comput. 7 073
[42] Zhao Y, Fung C H F, Qi B, Chen C and Lo H K 2008 Phys. Rev. A 78 042333
[43] Lydersen L,Wiechers C,Wittmann C, Elser D, Skaar J and Makarov V 2010 Nat. Photonics 4 686
[44] Wu Z H, Huang A Q, Chen H, Sun S H, Ding J F, Qiang X G, Fu X, Xu P and Wu J 2020 Opt. Express 28 25574
[45] Xu F H, Ma X F, Zhang Q, Lo H K and Pan J W 2020 Rev. Mod. Phys. 92 025002
[46] Gnanapandithan A, Qian L and Lo H K 2025 Phys. Rev. Lett. 134 130802
[47] Lo H K, Curty M and Qi B 2012 Phys. Rev. Lett. 108 130503
[48] Braunstein S L and Pirandola S 2012 Phys. Rev. Lett. 108 130502
[49] Xu F H, Curty M, Qi B and Lo H K 2013 New J. Phys. 15 113007
[50] Liu Y, Chen T Y, Wang L J, Liang H, Shentu G L, Wang J, Cui K, Yin H L, Liu N L, Li L, Ma X, Pelc J S, Fejer M M, Peng C Z, Zhang Q and Pan J W 2013 Phys. Rev. Lett. 111 130502
[51] Tang Z Y, Liao Z F, Xu F H, Qi B, Qian L and Lo H K 2014 Phys. Rev. Lett. 112 190503
[52] Yin H L, Chen T Y, Yu ZW, Liu H, You L X, Zhou Y H, Chen S J, Mao Y, Huang M Q, ZhangWJ, Chen H, Li M J, Nolan D, Zhou F, Jiang X, Wang Z, Wang X B and Pan J W 2016 Phys. Rev. Lett. 117 190501
[53] Tang G Z, Sun S H, Li C Y 2019 Chin. Phys. Lett. 36 070301
[54] Wei K J, Li W, Tan H, Li Y, Min H, Zhang W J, Li H, You L X, Wang Z, Jiang X, Chen T Y, Liao S K, Peng C Z, Xu F H and Pan J W 2020 Phys. Rev. X 10 031030
[55] Fan-Yuan G J, Lu F Y, Wang S, Yin Z Q, He D Y, Chen W, Wang Z H, Huang X J, Zhou Z, Wang Z H, Teng J, Guo G C and Han Z F 2022 Optica 9 812
[56] Zeng P, Zhou H Y, Wu W J and Ma X F 2022 Nat. Commun. 13 3903
[57] Xie Y M, Lu Y S, Weng C X, Cao X Y, Jia Z Y, Bao Y, Wang Y, Fu Y, Yin H L and Chen Z B 2022 PRX Quantum 3 020315
[58] Zhu H T, Huang Y, Liu H, Zeng P, Zou M, Dai Y, Tang S, Li H, You L X, Wang Z, Chen Y A, Ma X, Chen T Y, and Pan J W 2023 Phys. Rev. Lett. 130 030801
[59] Sun M H, Zhang C H, Ding H J, Zhou X Y, Li J and Wang Q 2023 Phys. Rev. Appl. 20 024029
[60] Lu F Y, Ye P, Wang Z H, Wang S, Yin Z Q, Wang R, Huang X J, Chen W, He D Y, Fan-Yuan G J, Guo G C and Han Z F 2023 Optica 10 520
[61] SunMS, Zhang C H, Zhang R, Zhou X Y, Li J andWang Q 2024 Chin. Phys. B 33 110302
[62] Zhan X H, Zhong Z Q, Ma J Y, Wang S, Zhang Q, Chen W, Bian Z F, Huang X J, Han Z F, Chou C W, Zhang L J and Guo G C 2025 npj Quantum Inf. 11 73
[63] Zhao Y M, Zhou C, Jiang X L, Lu Y F, Zhou Y,Wang H T,Wang Y, Li J J, Zhou Y Y, Li H and Bao W S 2025 Chin. Phys. B 34 050302
[64] Shao S F, Zhou L, Lin J P, Minder M, Ge C F, Xie Y M, Shen A, Yan Z, Yin H L, Yuan Z 2025 Phys. Rev. X 15 021066
[65] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
[66] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H and Zeilinger A 1997 Nature 390 575
[67] Bennett C H and Wiesner S J 1992 Phys. Rev. Lett. 69 2881
[68] Mattle K, Weinfurter H, Kwiat P G and Zeilinger A 1996 Phys. Rev. Lett. 76 4656
[69] Braunstein S L and Mann A 1995 Phys. Rev. A 51 R1727
[70] Calsamiglia J and Lütkenhaus N 2001 Appl. Phys. B 72 67
[71] Barreiro J T, Wei T C and Kwiat P G 2008 Nat. Phys. 4 282
[72] Hu X M, Guo Y, Liu B H, Huang Y F, Li C F and Guo G C 2018 Sci. Adv. 4 eaat9304
[73] Grice W P 2011 Phys. Rev. A 84 042331
[74] Ewert F and van Loock P 2014 Phys. Rev. Lett. 113 140403
[75] Bayerbach M J, D'Aurelio S E, van Loock P and Barz S 2023 Sci. Adv. 9 eadf4080
[76] Gottesman N L D, Lo H K and Preskill J 2004 Quantum Inf. Comput. 4 325
[77] Ma X F and Razavi M 2012 Phys. Rev. A 86 062319
[78] 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 and Pan J W 2019 Nat. Photonics 13 770
[79] Moczala-Dusanowska M, Dusanowski L, Iff O, Huber T, Kuhn S, Czyszanowski T, Schneider C and Höfling S 2020 ACS Photonics 7 3474

Measurement-device-independent quantum key distribution with entanglement-assisted linear Bell state measurement

Measurement-device-independent quantum key distribution with entanglement-assisted linear Bell state measurement

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