基于非高斯态区分探测的往返式离散调制连续变量量子密钥分发方案

吴晓东; 黄端

doi:10.7498/aps.72.20222253

摘要

往返式离散调制连续变量量子密钥分发, 无需使用两台独立的激光器也能本地生成本振光, 并且信号光与本振光均来自于同一台激光器, 在有效保证系统实际安全性的同时, 具有较好的同频特性. 此外, 该方案与高效纠错码具有良好的兼容性, 即使在低信噪比情况下也能获得较高的协商效率. 然而, 基于非可信信源模型的往返式光路结构存在较大的过噪声, 严重限制离散调制方案的最大传输距离. 针对这个问题, 本文提出基于非高斯态区分探测的往返式离散调制连续变量量子密钥分发方案, 即在探测端部署非高斯态区分探测器, 采用自适应测量方法并结合贝叶斯推论, 可以在满足低于标准量子极限错误概率的情况下无条件区分出基于四态离散调制的四种非正交相干态. 本文详细分析了所提出的基于非高斯态区分探测的往返式离散调制连续变量量子密钥分发方案的安全性, 包括渐近情况与有限长效应情况. 仿真结果表明所提出的方案相比于原始方案, 即使在有信源噪声的情况下, 其密钥率与最大传输距离仍然有明显的提升. 这些结果表明本方案能够有效降低往返式离散调制连续变量量子密钥分发方案中非可信信源噪声对方案性能的负面影响, 在保证系统实际安全性的同时, 实现更高效、更远传输距离的量子密钥分发.

关键词:

Abstract

Plug-and-play discrete modulation continuous variable quantum key distribution can generate local oscillator light locally without using two independent lasers, and both signal light and local oscillator are generated from the same laser, which can effectively ensure the practical security of the system and have a completely identical frequency characteristic. In addition, this scheme has good compatibility with efficient error correction codes, and can achieve high reconciliation efficiency even at low signal-to-noise ratio. However, there exists large excess noise in the plug-and-play configuration based on the untrusted source model, which seriously limits the maximum transmission distance of the discrete modulation scheme. To solve this problem, we propose a plug-and-play discrete modulation continuous variable quantum key distribution based on non-Gaussian state-discrimination detection. That is to say, a non-Gaussian state-discrimination detector is deployed at the receiver. With adaptive measurement method and Bayesian inference, four non-orthogonal coherent states which are based on four-state discrete modulation can be unconditionally distinguished on condition that the error probability is lower than the standard quantum limit. We analyze the security of the proposed protocol by considering both asymptotic limit and finite-size effect. Simulation results show that the secret key rate and maximum transmission distance are significantly enhanced by using no-Gaussian state-discrimination detection even under the influence of the untrusted source noise compared with the original plug-and-play discrete modulation continuous variable quantum key distribution. These results indicate that the proposed scheme can effectively reduce the negative influence of the untrust source noise on the performance of the plug-and-play discrete modulation continuous variable quantum key distribution protocol. The proposed protocol can not only ensure the practical security of the system, but also achieve more efficient and longer transmission distance quantum key distribution.

Keywords:

plug-and-play /
discrete modulation /
continuous variable quantum key distribution /
non-Gaussian state-discrimination detection

作者及机构信息

吴晓东¹,
黄端²

1.
福建工程学院管理学院, 福州　350118

2.
中南大学计算机学院, 长沙　410083

通信作者: 黄端, duanhuang@csu.edu.cn

基金项目: 国家自然科学基金(批准号: 61972418, 61977062, 61801522)和福建工程学院科研启动基金(批准号: GY-Z22042)资助的课题.

Authors and contacts

Wu Xiao-Dong¹,
Huang Duan²

1.
School of Management, Fujian University of Technology, Fuzhou 350118, China

2.
School of Computer Science and Engineering, Central South University, Changsha 410083, China

Corresponding author: Huang Duan, duanhuang@csu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61972418, 61977062, 61801522) and the Scientific Research Initiation Fund of Fujian University of Technology, China (Grant No. GY-Z22042).

文章全文

参考文献

[1]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
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[12]	钟海, 叶炜, 吴晓东, 郭迎 2021 物理学报 70 020301 Google Scholar Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301 Google Scholar
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[40]	Navascués M, Acín A 2005 Phys. Rev. Lett. 94 020505 Google Scholar
[41]	García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503 Google Scholar
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[43]	Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504 Google Scholar
[44]	Leverrier A, Grosshans F, Grangier P 2010 Phys. Rev. A 81 062343 Google Scholar
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施引文献

图 1 基于非高斯态区分探测的往返式离散调制CV-QKD制备-测量方案图. DM为离散调制, RNG为随机数发生器, M为调制器, QPSK为正交相移键控, PIA为相位非敏感放大器, FM为法拉第镜, BS为分束器, LO为本振光, $ T $表示非可信信道的透过率, $ \xi $表示信道过噪声, g表示相位非敏感放大器的增益参数

Fig. 1. Prepare-and-measure version of plug-and-play discrete modulation CV-QKD protocol based on non-Gaussian state-discrimination detection. DM, discrete modulation; RNG, random number generator; M, modulator; QPSK, quadrature phase shift keying; PIA, phase insensitive amplifier; FM, Faraday mirror; BS, beam splitter; LO, local oscillator; $ T $, transmission efficiency; $ \xi $, channel excess noise; g, gain parameters of phase insensitive amplifier.

下载: 全尺寸图片幻灯片

图 2 基于非高斯态区分探测的往返式离散调制CV-QKD纠缠模型原理图

Fig. 2. Schematic diagram of the entanglement-based (EB) model of plug-and-play discrete modulation CV-QKD protocol based on state-discrimination detection.

下载: 全尺寸图片幻灯片

图 3 非高斯态区分探测器原理图. PNRD为光子数分辨探测器

Fig. 3. Schematic diagram of non-Gaussian state discrimination detector. PNRD, photon-number-resolving detector.

下载: 全尺寸图片幻灯片

图 4 不同增益参数$g$下基于非高斯态区分探测的往返式离散调制CV-QKD方案的渐近密钥率和传输距离的关系

Fig. 4. The relationship between the asymptotic secret key rate of plug-and-play discrete modulation CV-QKD protocol based on non-Gaussian state-discrimination detection and the transmission distance under different gain $g$.

下载: 全尺寸图片幻灯片

图 5 在实际信源($g = 1.005$)与不同传输距离$L$下, 基于非高斯态区分探测的往返式离散调制CV-QKD方案的渐近密钥率与协商效率的关系

Fig. 5. The relationship between the asymptotic secret key rate of plug-and-play discrete modulation CV-QKD protocol based on non-Gaussian state-discrimination detection and the reconciliation efficiency under practical source($g = 1.005$) and different transmission distance $L$.

下载: 全尺寸图片幻灯片

图 6 不同传输距离下L下, 基于非高斯态区分探测的往返式离散调制CV-QKD方案的信噪比与增益参数g (不同的信源条件)的关系

Fig. 6. The relationship between the signal-to-noise ratio of plug-and-play discrete modulation CV-QKD protocol based on non-Gaussian state-discrimination detection and the gain g (different source conditions) under different transmission distance L.

下载: 全尺寸图片幻灯片

图 7 在不同的有效数据总长度$F$下基于非高斯态区分探测的往返式离散调制CV-QKD方案有限长密钥率与传输距离的关系　(a) $g = 1$; (b) $g = 1.003$; (c) $g = 1.005$; (d) $g = 1.01$

Fig. 7. The relationship between the finite-size secret key rate of plug-and-play discrete modulation CV-QKD protocol based on non-Gaussian state-discrimination detection and the transmission distance under different total exchanged signals $F$: (a) $g = 1$; (b) $g = 1.003$; (c) $g = 1.005$; (d) $g = 1.01$.

下载: 全尺寸图片幻灯片

[1]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
[2]	Pirandola S, Andersen U L, Banchi L, et al. 2020 Adv. Opt. Photon. 12 1012 Google Scholar
[3]	Liu H, Jiang C, Zhu H T, et al. 2021 Phys. Rev. Lett. 126 250502 Google Scholar
[4]	Lo H K, Chau H F 1999 Science 283 2050 Google Scholar
[5]	Shor P W, Preskill J 2000 Phys. Rev. Lett. 85 441 Google Scholar
[6]	Yin J, Li Y H, Liao S K, et al. 2020 Nature 582 501 Google Scholar
[7]	Fang X T, Zeng P, Liu H, et al. 2020 Nat. Photonics 14 422 Google Scholar
[8]	Chen J P, Zhang C, Liu Y, et al. 2021 Nat. Photonics 15 570 Google Scholar
[9]	Laudenbach F, Pacher C, Fung C H F, Poppe A, Peev M, Schrenk B, Hentschel M, Walther P, Hübel H 2018 Adv. Quantum Technol. 1 1800011 Google Scholar
[10]	Wu X D, Wang Y J, Huang D, Guo Y 2020 Front. Phys. 15 31601 Google Scholar
[11]	Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902 Google Scholar
[12]	钟海, 叶炜, 吴晓东, 郭迎 2021 物理学报 70 020301 Google Scholar Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301 Google Scholar
[13]	Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature (London) 421 238
[14]	Huang D, Huang P, Lin D, Zeng G 2016 Sci. Rep. 6 19201 Google Scholar
[15]	Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378 Google Scholar
[16]	Huang D, Lin D, Wang C, Liu W, Fang S, Peng J, Huang P, Zeng G 2015 Opt. Express 23 17511 Google Scholar
[17]	Zhang Y, Chen Z, Pirandola S, Wang X, Zhou C, Chu B, Zhao Y, Xu B, Yu S, Guo H 2020 Phys. Rev. Lett. 125 010502 Google Scholar
[18]	Huang D, Huang P, Li H, Wang T, Zhou Y, Zeng G 2016 Opt. Lett. 41 3511 Google Scholar
[19]	Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 88 022339 Google Scholar
[20]	Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 87 052309 Google Scholar
[21]	Jouguet P, Kunz-Jacques S, Diamanti E 2013 Phys. Rev. A 87 062313 Google Scholar
[22]	Qin H, Kumar R, Alléaume R 2016 Phys. Rev. A 94 012325 Google Scholar
[23]	Qi B, Lougovski P, Pooser R, Grice W, Bobrek M 2015 Phys. Rev. X 5 041009 Google Scholar
[24]	Soh D B S, Brif C, Coles P J, Lütkenhaus N, Camacho R M, Urayama J, Sarovar M 2015 Phys. Rev. X 5 041010 Google Scholar
[25]	Huang D, Lin D K, Huang P, Zeng G H 2015 Opt. Lett. 40 3695 Google Scholar
[26]	Marie A, Alléaume R 2017 Phys. Rev. A 95 012316 Google Scholar
[27]	Wang T, Huang P, Zhou Y, Liu W, Zeng G 2018 Phys. Rev. A 97 012310 Google Scholar
[28]	Wu X, Wang Y, Guo Y, Zhong H, Huang D 2021 Phys. Rev. A 103 032604 Google Scholar
[29]	Huang D, Huang P, Wang T, Li H, Zhou Y, Zeng G 2016 Phys. Rev. A 94 032305 Google Scholar
[30]	Silberhorn C, Ralph T C, Lütkenhaus N, Leuchs G 2002 Phys. Rev. Lett. 89 167901 Google Scholar
[31]	Leverrier A, Grangier P 2009 Phys. Rev. Lett. 102 180504 Google Scholar
[32]	Becerra F E, Fan J, Baumgartner G, Goldhar J, Kosloski J T, Migdall A 2013 Nat. Photonics 7 147 Google Scholar
[33]	Becerra F E, Fan J, Migdall A 2013 Nat. Commun. 4 2028 Google Scholar
[34]	Becerra F E, Fan J, Baumgartner G, Polyakov S V, Goldhar J, Kosloski J T, Migdall A 2011 Phys. Rev. A 84 062324 Google Scholar
[35]	Helstrom C W 1976 Quantum Detection and Estimation Theory (Mathematics in Science and Engineering) (Vol. 123) (New York: Academic)
[36]	Liao Q, Guo Y, Huang D, Huang P, Zeng G 2018 New J. Phys. 20 023015 Google Scholar
[37]	Shen Y, Peng X, Yang J, Guo H 2011 Phys. Rev. A 83 052304 Google Scholar
[38]	Wu X D, Wang Y J, Zhong H, Liao Q, Guo Y 2019 Front. Phys. 14 41501 Google Scholar
[39]	Wu X, Wang Y, Zhong H, Ye W, Huang D, Guo Y 2020 Quantum Inf. Process. 19 234 Google Scholar
[40]	Navascués M, Acín A 2005 Phys. Rev. Lett. 94 020505 Google Scholar
[41]	García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503 Google Scholar
[42]	Pirandola S, Braunstein S L, Lloyd S 2008 Phys. Rev. Lett. 101 200504 Google Scholar
[43]	Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504 Google Scholar
[44]	Leverrier A, Grosshans F, Grangier P 2010 Phys. Rev. A 81 062343 Google Scholar
[45]	Pirandola S, Laurenza R, Ottaviani C, Banchi L 2017 Nat. Commun. 8 15043 Google Scholar

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基于非高斯态区分探测的往返式离散调制连续变量量子密钥分发方案