基于实际探测器补偿的离散调制连续变量测量设备无关量子密钥分发方案

吴晓东; 黄端; 黄鹏; 郭迎

doi:10.7498/aps.71.20221072

摘要

由于离散调制连续变量测量设备无关量子密钥分发方案与高效纠错码具有良好的兼容性, 因此即使在低信噪比条件下, 也具备较高的协商效率, 并且其实现条件相比于高斯调制方案更加简单. 然而, 实验中常用的零差探测器的量子效率仅为0.6, 这会严重影响离散调制连续变量测量设备无关量子密钥分发方案的实际应用性能. 鉴于此, 本文提出基于实际探测器补偿的离散调制连续变量测量设备无关量子密钥分发方案, 即在该方案中对两条量子信道的输出端各采用一个相位敏感放大器用于补偿相对应的实际零差探测器. 仿真结果表明采用相位敏感放大器能够很好地补偿实际零差探测器的量子效率, 有效提升基于实际探测器的离散调制连续变量测量设备无关量子密钥分发方案的密钥率和安全传输距离, 为推动离散调制连续变量测量设备无关量子密钥分发方案的实用化发展提供了一个有效而实用的方法.

关键词:

Abstract

Discrete modulation continuous variable measurement device independent quantum key distribution scheme has good compatibility with efficient error correction codes, which leads to high reconciliation efficiency even at low signal-to-noise ratio. Besides, the implementation of this protocol is simpler than that of Gaussian modulation scheme. However, the quantum efficiency of homodyne detector commonly used in the experiment is only 0.6, which will seriously affect the practical application performance of discrete modulation continuous variable measurement device independent quantum key distribution scheme. To solve this problem, we propose a discrete modulation continuous variable measurement device independent quantum key distribution scheme based on realistic detector compensation. In our scheme, for the outputs of two quantum channels, each adopts a phase sensitive amplifier to compensate for the corresponding realistic homodyne detector. The simulation results show that the phase sensitive amplifier can well compensate for the quantum efficiency of the realistic detector and effectively improve the performance of the discrete modulation continuous variable measurement device independent quantum key distribution scheme with realistic detector in terms of secret key rate and secure transmission distance. The proposed protocol provides an effective method for promoting the practical development of the discrete modulation continuous variable measurement device independent quantum key distribution scheme.

Keywords:

discrete modulation /
continuous variable /
measurement device independent quantum key distribution /
realistic detector compensation

作者及机构信息

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

3.
上海交通大学区域光纤通信网与新型光通信系统国家重点实验室, 量子传感与信息处理中心, 上海　200240

4.
中南大学自动化学院, 长沙　410083

通信作者: 黄端, duanhuang@csu.edu.cn ; 黄鹏, huang.peng@sjtu.edu.cn ;

基金项目: 国家自然科学基金(批准号: 61871407, 61872390, 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

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

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

3.
State Key Laboratory of Advanced Optical Communication Systems and Networks, Center for Quantum Sensing and Information Processing, Shanghai Jiao Tong University, Shanghai 200240, China

4.
School of Automation, Central South University, Changsha 410083, China

Corresponding author: Huang Duan, duanhuang@csu.edu.cn ; Huang Peng, huang.peng@sjtu.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61871407, 61872390, 61801522) and the Scientific Research Initiation Fund of Fujian University of Technology, China (Grant No. GY-Z22042).

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参考文献

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施引文献

图 1 基于实际探测器的离散调制CV-MDI-QKD方案图, $D(\delta )$表示置换操作

Fig. 1. Schematic diagram of the discrete modulation CV-MDI-QKD based on realistic detector, $D(\delta )$ represents displacement operation.

下载: 全尺寸图片幻灯片

图 2 $W$(${W_4}$和${W_{{\text{EPR}}}}$)与调制方差${V_{\text{M}}}$的关系

Fig. 2. Relationship between $W$(${W_4}$ and ${W_{{\text{EPR}}}}$) and the modulation variance ${V_{\text{M}}}$.

下载: 全尺寸图片幻灯片

图 3 基于PSA的离散调制CV-MDI-QKD实际探测器补偿方案图, PSA为相位敏感放大器

Fig. 3. Schematic diagram of discrete modulation CV-MDI-QKD with realistic detector compensation based on PSA, where PSA is the phase-sensitive amplifier.

下载: 全尺寸图片幻灯片

图 4 在对称情况以及不同的PSA增益参数$G$下所提出方案的安全密钥率与传输距离的关系

Fig. 4. Relationship between the security key rate and transmission distance of the proposed scheme in the symmetric case with different PSA gain $G$.

下载: 全尺寸图片幻灯片

图 5 极端非对称情况下所提出方案的安全密钥率与PSA增益参数$G$及传输距离${L_{AC}}$的关系

Fig. 5. Relationship between the secret key rate and the PSA gain$G$, transmission distance ${L_{AC}}$ of the proposed scheme in the extreme asymmetric case.

下载: 全尺寸图片幻灯片

图 6 极端非对称情况以及不同的PSA增益参数$G$下所提出方案的安全密钥率与传输距离的关系

Fig. 6. Relationship between the secret key rate and the transmission distance of the proposed scheme in the extreme asymmetric case with different PSA gain G.

下载: 全尺寸图片幻灯片

图 7 极端非对称情况以及不同PSA增益参数$G$下所提出方案的安全密钥率与协商效率$\beta $的关系

Fig. 7. Relationship between the secret key rate and the reconciliation efficiency $\beta $ of the proposed scheme in the extreme asymmetric case with different PSA gain $G$.

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]	Lo H K, Curty M, Tamaki K 2014 Nat. Photonics 8 595 Google Scholar
[3]	Liu H, Jiang C, Zhu H T, Zou M, Yu Z W, Hu X L, Xu H, Ma S, Han Z, Chen J P, Dai Y, Tang S B, Zhang W, Li H, You L, Wang Z, Hua Y, Hu H, Zhang H, Zhou F, Zhang Q, Wang X B, Chen T Y, Pan J W 2021 Phys. Rev. Lett. 126 250502 Google Scholar
[4]	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. Photon. 12 1012 Google Scholar
[5]	Chen J P, Zhang C, Liu Y, Jiang C, Zhang W J, Han Z Y, Ma S Z, Hu X L, Li Y H, Liu H, Zhou F, Jiang H F, Chen T Y, Li H, You L X, Wang Z, Wang X B, Zhang Q, Pan J W 2021 Nat. Photonics 15 570 Google Scholar
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[8]	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
[9]	Wu X D, Wang Y J, Zhong H, Liao Q, Guo Y 2019 Front. Phys. 14 41501 Google Scholar
[10]	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
[11]	Wu X, Wang Y, Guo Y, Zhong H, Huang D 2021 Phys. Rev. A 103 032604 Google Scholar
[12]	Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902 Google Scholar
[13]	Wang T, Zuo Z, Li L, Huang P, Guo Y, Zeng G 2022 Phys. Rev. Appl. 18 014064 Google Scholar
[14]	Liu C, Zhu C, Nie M, Yang H, Pei C 2022 Opt. Express 30 14798 Google Scholar
[15]	Jing F, Liu X, Wang X, Lu Y, Wu T, Li K, Dong C 2022 Opt. Express 30 8075 Google Scholar
[16]	Sarmiento S, Etcheverry S, Aldama J, López I H, Vidarte L T, Xavier G B, Nolan D A, Stone J S, Li M J, Loeber D, Pruneri V 2022 New J. Phys. 24 063011 Google Scholar
[17]	García-Patrón R, Cerf N J 2006 Phys. Rev. Lett. 97 190503 Google Scholar
[18]	Navascués M, Grosshans F, Acín A 2006 Phys. Rev. Lett. 97 190502 Google Scholar
[19]	Pirandola S, Braunstein S L, Lloyd S 2008 Phys. Rev. Lett. 101 200504 Google Scholar
[20]	Renner R, Cirac J I 2009 Phys. Rev. Lett. 102 110504 Google Scholar
[21]	Leverrier A, Grosshans F, Grangier P 2010 Phys. Rev. A 81 062343 Google Scholar
[22]	Leverrier A 2015 Phys. Rev. Lett. 114 070501 Google Scholar
[23]	Huang D, Huang P, Lin D, Zeng G 2016 Sci. Rep. 6 19201 Google Scholar
[24]	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
[25]	Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378 Google Scholar
[26]	Huang D, Lin D, Wang C, Liu W, Fang S, Peng J, Huang P, Zeng G 2015 Opt. Express 23 17511 Google Scholar
[27]	Huang D, Huang P, Li H, Wang T, Zhou Y, Zeng G 2016 Opt. Lett. 41 3511 Google Scholar
[28]	Filip R 2008 Phys. Rev. A 77 022310 Google Scholar
[29]	Yuan Z L, Dynes J F, Shields A J 2010 Nat. Photonics 4 800 Google Scholar
[30]	Jouguet P, Kunz-Jacques S, Diamanti E 2013 Phys. Rev. A 87 062313 Google Scholar
[31]	Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 88 022339 Google Scholar
[32]	Ma X C, Sun S H, Jiang M S, Liang L M 2013 Phys. Rev. A 87 052309 Google Scholar
[33]	Qin H, Kumar R, Alléaume R 2016 Phys. Rev. A 94 012325 Google Scholar
[34]	Braunstein S L, Pirandola S 2012 Phys. Rev. Lett. 108 130502 Google Scholar
[35]	Lo H K, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503 Google Scholar
[36]	Wang X B 2013 Phys. Rev. A 87 012320 Google Scholar
[37]	Xu F, Curty M, Qi B, Lo H K 2013 New J. Phys. 15 113007 Google Scholar
[38]	Curty M, Xu F, Cui W, Lim C C W, Tamaki K, Lo H K 2014 Nat. Commun. 5 3732 Google Scholar
[39]	Lupo C, Ottaviani C, Papanastasiou P, Pirandola S 2018 Phys. Rev. Lett. 120 220505 Google Scholar
[40]	Ferreira da S T, Vitoreti D, Xavier G B, do Amaral G C, Temporao G P, von derWeid J P 2013 Phys. Rev. A 88 052303 Google Scholar
[41]	Cao Y, Li Y H, Yang K X, Jiang Y F, Li S L, Hu X L, Abulizi M, Li C L, Zhang W, Sun Q C, Liu W Y, Jiang X, Liao S K, Ren J G, Li H, You L, Wang Z, Yin J, Lu C Y, Wang X B, Zhang Q, Peng C Z, Pan J W 2020 Phys. Rev. Lett. 125 260503 Google Scholar
[42]	Xu F, Qi B, Liao Z, Lo H K 2013 Appl. Phys. Lett. 103 061101 Google Scholar
[43]	Li Z, Zhang Y C, Xu F, Peng X, Guo H 2014 Phys. Rev. A 89 052301 Google Scholar
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[45]	Zhang Y C, Li Z, Yu S, Gu W, Peng X, Guo H 2014 Phys. Rev. A 90 052325 Google Scholar
[46]	Wu X D, Wang Y J, Huang D, Guo Y 2020 Front. Phys. 15 31601 Google Scholar
[47]	Pirandola S, Ottaviani C, Spedalieri G, Weedbrook C, Braunstein S L, Lloyd S, Gehring T, Jacobsen C S, Andersen U L 2015 Nat. Photonics 9 397 Google Scholar
[48]	Richardson T J, Shokrollahi M A, Urbanke R 2001 IEEE Trans. Inf. Theory 47 619 Google Scholar
[49]	Leverrier A, Alléaume R, Boutros J, Zémor G, Grangier P 2008 Phys. Rev. A 77 042325 Google Scholar
[50]	Jouguet P, Kunz-Jacques S, Leverrier A 2011 Phys. Rev. A 84 062317 Google Scholar
[51]	Milicevic M, Chen F, Zhang L M, Gulak P. G 2018 npj Quantum Inf. 4 21 Google Scholar
[52]	Ma H X, Huang P, Bai D Y, Wang T, Wang S Y, Bao W S, Zeng G H 2019 Phys. Rev. A 99 022322 Google Scholar
[53]	Lodewyck J, Bloch M, García-Patrón R, Fossier S, Karpov E, Diamanti E, Debuisschert T, Cerf N J, Tualle-Brouri R, McLaughlin S W, Grangier P 2007 Phys. Rev. A 76 042305 Google Scholar
[54]	Leverrier A, Grangier P 2009 Phys. Rev. Lett. 102 180504 Google Scholar
[55]	Polkinghorne R E S, Ralph T C 1999 Phys. Rev. Lett. 83 2095 Google Scholar
[56]	Pirandola S 2013 New J. Phys. 15 113046 Google Scholar
[57]	Fossier S, Diamanti E, Debuisschert T, Tualle-Brouri R, Grangier P 2009 J. Phys. B 42 114014 Google Scholar
[58]	Pirandola S, Laurenza R, Ottaviani C, Banchi L 2017 Nat. Commun. 8 15043 Google Scholar

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基于实际探测器补偿的离散调制连续变量测量设备无关量子密钥分发方案