基于非理想测量基选择的水下连续变量量子密钥分发方案

吴晓东; 黄端

doi:10.7498/aps.73.20240804

摘要

在基于零差探测的水下连续变量量子密钥分发系统中, 测量基选择是必不可少的步骤. 然而在实际中, 接收端数模转换器的带宽有限, 这会导致测量基选择出现缺陷, 即接收方无法在相位调制器上精确地调制出相应的相位角来进行测量基选择以实施零差探测. 非理想测量基选择会引入额外的过噪声, 影响水下连续变量量子密钥分发方案的安全性. 针对这个问题, 本文提出基于非理想测量基选择的水下连续变量量子密钥分发方案, 详细分析非理想测量基选择对水下连续变量量子密钥分发系统性能的影响. 研究结果表明, 由非理想测量基选择所引入的过噪声能够降低水下高斯调制量子密钥分发的密钥率与最大传输距离, 因而降低系统的安全性. 为了实现可靠的水下连续变量量子密钥分发, 本文对非理想测量基选择所引入的额外过噪声进行定量分析并获得其安全界限, 并且考虑不同海水深度对所提出方案安全界限的影响, 有效地解决由非理想测量基选择所带来的安全隐患. 此外, 对所提出的方案, 本文不仅考虑了其渐近安全性, 也考虑了其组合安全性, 后者能够获得比前者更紧的性能曲线. 本文所提出的方案旨在推动水下连续变量量子密钥分发系统的实用化进程, 为全球量子通信网络的水下通信中水信道参数的准确评估提供理论指导.

关键词:

Abstract

Measurement basis choice is an essential step in the underwater continuous variable quantum key distribution system based on homodyne detection. However, in practice, finite bandwidth of analog-to-digital converter on the receiver’s side is limited, which can result in defects in the measurement basis choice. That is, the receiver cannot accurately modulate the corresponding phase angle on the phase modulator for measurement basis choice to implement homodyne detection. The imperfect measurement basis choice will introduce extra excess noise, which affects the security of underwater continuous variable quantum key distribution scheme. To solve this problem, we propose an underwater continuous variable quantum key distribution scheme based on imperfect measurement basis choice, and analyze the influence of imperfect measurement basis choice on the performance of underwater continuous variable quantum key distribution system in detail. The research results indicate that the extra excess noise introduced by imperfect measurement basis choice can reduce the secret key rate and maximum transmission distance of the underwater Gaussian modulated quantum key distribution, thus reducing the security of the system. In order to achieve reliable underwater continuous variable quantum key distribution, we quantitatively analyze the extra excess noise introduced by choosing the imperfect measurement basis and obtain its security limit. Besides, we also consider the influence of different seawater depths on the security limit of the proposed scheme, effectively solving the security risks caused by the imperfect measurement basis choice. Furthermore, for the proposed scheme, we consider not only its asymptotic security case but also its composable security case, and the performance curves obtained in the latter are tighter than that achieved in the former. The proposed scheme aims to promote the practical process of underwater continuous variable quantum key distribution system and provide theoretical guidance for accurately evaluating the water channel parameters in underwater communication of global quantum communication networks.

Keywords:

imperfect measurement basis choice /
continuous variable quantum key distribution /
seawater channel /
seawater depth

作者及机构信息

吴晓东¹,
黄端²

1.
福建理工大学管理学院, 福州　350118

2.
中南大学电子信息学院, 长沙　410083

通信作者: 黄端, duanhuang@csu.edu.cn

基金项目: 福建省自然科学基金(批准号: 2023J01940)和福建理工大学科研启动基金 (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 Electronic Information, Central South University, Changsha 410083, China

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

Funds: Project supported by the Fujian Provincial Natural Science Foundation of China (Grant No. 2023J01940) and the Scientific Research Initiation Fund of Fujian University of Technology, China (Grant No. GY-Z22042).

文章全文 : translate this paragraph

参考文献

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施引文献

图 1 基于非理想测量基选择的水下CV-QKD制备-测量方案图. RNG为随机数发生器, AM为振幅调制器, PM为相位调制器, MBC表示测量基选择, $ {T_{\text{s}}} $表示海水信道的透过率, $ {\xi _{\text{s}}} $表示海水信道过噪声

Fig. 1. Prepare-and-measure version of underwater continuous variable quantum key distribution scheme based on imperfect measurement basis choice. RNG, random number generator; AM, amplitude modulator; PM, phase modulator; MBC, measurement basis choice; $ {T_{\text{s}}} $, the transmittance of seawater channel; $ {\xi _{\text{s}}} $, the excess noise of seawater channel.

下载: 全尺寸图片幻灯片

图 2 基于非理想测量基选择的水下CV-QKD纠缠模型原理图(QM为量子存储器)

Fig. 2. Schematic diagram of the entanglement-based model of underwater continuous variable quantum key distribution scheme based on imperfect basis choice (QM, quantum memory).

下载: 全尺寸图片幻灯片

图 3 零差探测器的探测原理图(LO为本振光, PM为相位调制器, BS为分束器, PD₁₍₂₎为光电探测器)

Fig. 3. Principle of balanced homodyne detector. LO, local oscillator; PM, phase modulator; BS, beam splitter; PD₁₍₂₎, photodetector.

下载: 全尺寸图片幻灯片

图 4 所提出方案的渐近密钥率与传输距离在不同参数$ \mu $下的关系

Fig. 4. Relationship between the asymptotic secret key rate of the proposed scheme and the transmission distance under different parameters $ \mu $.

下载: 全尺寸图片幻灯片

图 5 所提出方案的渐近密钥率与协商效率在不同参数$ \mu $下的关系

Fig. 5. Relationship between the asymptotic secret key rate of the proposed scheme and the reconciliation efficiency under different parameters $ \mu $.

下载: 全尺寸图片幻灯片

图 6 所提出方案的密钥率与参数$ \mu $在不同海水深度$ h $下的关系

Fig. 6. Relationship between the asymptotic secret key rate of the proposed scheme and the parameter $ \mu $ under different seawater depths $ h $.

下载: 全尺寸图片幻灯片

图 7 非理想测量基选择情况下所提出的方案与基于BL模型的水下CV-QKD方案性能比较

Fig. 7. Performance comparison between the proposed scheme and the underwater CV-QKD scheme based on BL model under imperfect measurement basis choice.

下载: 全尺寸图片幻灯片

图 8 所提出方案的组合密钥率与用于交换的有效脉冲总数在不同参数$ \mu $下的关系

Fig. 8. Relationship between the composable secret key rate of the proposed scheme and the number of exchanged signals under different parameters $ \mu $.

下载: 全尺寸图片幻灯片

图 9 非理想测量基选择情况下所提出的方案与基于BL模型的水下CV-QKD方案组合密钥率比较

Fig. 9. Composable secret key rate comparison between the proposed scheme and the underwater CV-QKD scheme based on BL model under imperfect measurement basis choice.

下载: 全尺寸图片幻灯片

map

[1]	Zeng Z, Fu S, Zhang H, Dong Y, Cheng J 2017 IEEE Commun. Surv. Tutorials 19 204 Google Scholar
[2]	Hanson F, Radic S 2008 Appl. Opt. 47 277 Google Scholar
[3]	Kong M, Wang J, Chen Y, Ali T, Sarwar R, Qiu Y, Wang S, Han J, Xu J 2017 Opt. Express 25 21509 Google Scholar
[4]	Wang J, Lu C, Li S, Xu Z 2019 Opt. Express 27 12171 Google Scholar
[5]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
[6]	Pirandola S, Andersen U L, Banchi L, Berta M, Bunandar D, Colbeck R, Englund D, Gehring T, Lupo C, Ottaviani C, Pereira J L, Razavi M, Shaari J S, Tomamichel M, Usenko V C, Vallone G, Villoresi P, Wallden P 2020 Adv. Opt. Photonics 12 1012 Google Scholar
[7]	Liu Y, Zhang W J, Jiang C, Chen J P, Zhang C, Pan W X, Ma D, Dong H, Xiong J M, Zhang C J, Li H, Wang R C, Wu J, Chen T Y, You L, Wang X B, Zhang Q, Pan J W 2023 Phys. Rev. Lett. 130 210801 Google Scholar
[8]	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, Pan J W 2023 Nat. Photonics 17 416 Google Scholar
[9]	Zahidy M, Mikkelsen M T, Müller R, Lio B D, Krehbiel M, Wang Y, Bart N, Wieck A D, Ludwig A, Galili M, Forchhammer S, Lodahl P, Oxenløwe L K, Bacco D, Midolo L 2024 npj Quantum Inf. 10 2 Google Scholar
[10]	Zhu H T, Huang Y, Liu H, Zeng P, Zou M, Dai Y, Tang S, Li H, You L, Wang Z, Chen Y A, Ma X, Chen T Y, Pan J W 2023 Phys. Rev. Lett. 130 030801 Google Scholar
[11]	Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902 Google Scholar
[12]	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
[13]	Zhang Y, Bian Y, Li Z, Yu S, Guo H 2024 Appl. Phys. Rev. 11 011318 Google Scholar
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[15]	Wu X D, Wang Y J, Zhong H, Liao Q, Guo Y 2019 Front. Phys. 14 41501 Google Scholar
[16]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621 Google Scholar
[17]	Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504 Google Scholar
[18]	Leverrier A, Grosshans F, Grangier P 2010 Phys. Rev. A 81 062343 Google Scholar
[19]	Leverrier A, García-Patrón R, Renner R, Cerf N J 2013 Phys. Rev. Lett. 110 030502 Google Scholar
[20]	Leverrier A 2015 Phys. Rev. Lett. 114 070501 Google Scholar
[21]	Leverrier A 2017 Phys. Rev. Lett. 118 200501 Google Scholar
[22]	Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature 421 238 Google Scholar
[23]	Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378 Google Scholar
[24]	Huang D, Lin D, Wang C, Liu W, Fang S, Peng J, Huang P, Zeng G 2015 Opt. Express 23 17511 Google Scholar
[25]	Huang D, Huang P, Lin D , Zeng G 2016 Sci. Rep. 6 19201 Google Scholar
[26]	Zhang G, Haw J Y, Cai H, Xu F, Assad S M, Fitzsimons J F, Zhou X, Zhang Y, Yu S, Wu J, Ser W, Kwek L C, Liu A Q 2019 Nat. Photonics 13 839 Google Scholar
[27]	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
[28]	Williams B P, Qi B, Alshowkan M, Evans P G, Peters N A 2024 Phys. Rev. Appl. 21 014056 Google Scholar
[29]	Hajomer A A E, Derkach I, Jain N, Chin H M, Andersen U L, Gehring T 2024 Sci. Adv. 10 eadi9474 Google Scholar
[30]	Grice W P, Qi B 2019 Phys. Rev. A 100 022339 Google Scholar
[31]	吴晓东, 黄端 2024 73 020304 Google Scholar Wu X D, Huang D 2024 Acta Phys. Sin. 73 020304 Google Scholar
[32]	Zhao W, Shi R, Wu X, Wang F, Ruan X 2023 Opt. Express 31 17003 Google Scholar
[33]	Shi P, Zhao S C, Gu Y J, Li W D 2015 J. Opt. Soc. Am. A: 32 349 Google Scholar
[34]	Zhao S C, Han X H, Xiao Y, Shen Y, Gu Y J, Li W D 2019 J. Opt. Soc. Am. A: 36 883 Google Scholar
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[36]	Feng Z, Li S, Xu Z 2021 Opt. Express 29 8725 Google Scholar
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[38]	Hu C Q, Yan Z Q, Gao J, Li Z M, Zhou H, Dou J P, Jin X M 2021 Phys. Rev. Appl. 15 024060 Google Scholar
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[41]	Xie C L, Guo Y, Wang Y J, Huang D, Zhang L 2018 Chin. Phys. Lett. 35 090302 Google Scholar
[42]	Ruan X, Zhang H, Zhao W, Wang X, Li X, Guo Y 2019 Appl. Sci. 9 4956 Google Scholar
[43]	Mao Y, Wu X, Huang W, Liao Q, Deng H, Wang Y, Guo Y 2020 Appl. Sci. 10 5744 Google Scholar
[44]	Xiang Y, Wang Y, Ruan X, Zuo Z, Guo Y 2021 Phys. Scr. 96 065103 Google Scholar
[45]	Tang X, Chen Z, Zhao Z, Kumar R, Dong Y 2022 Opt. Express 30 32428 Google Scholar
[46]	Liu W, Peng J, Qi J, Cao Z, He C 2020 Laser Phys. Lett. 17 055203 Google Scholar
[47]	Gilerson A, Zhou J, Hlaing S, Ioannou I, Schalles J, Gross B, Moshary F, Ahmed S 2007 Opt. Express 15 15702 Google Scholar
[48]	Gariano J, Djordjevic I B 2019 Opt. Express 27 3055 Google Scholar
[49]	Fossier S, Diamanti E, Debuisschert T, Tualle-Brouri R, Grangier P 2009 J. Phys. B: At. Mol. Opt. Phys. 42 114014 Google Scholar
[50]	Prieur L, Sathyendranath S 1981 Limnol. Oceanogr. 26 671 Google Scholar
[51]	Uitz J, Claustre H, Morel A, Hooker S B 2006 J. Geophys. Res. Oceans. 111 C08005 Google Scholar

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