一维高斯调制连续变量量子密钥分发现实源强度误差的影响

王普; 白增亮; 常利伟

doi:10.7498/aps.74.20250025

摘要

本文深入地研究了一维高斯调制连续变量量子密钥分发系统在源强度误差下的现实安全性和性能表现. 详细地分析了源强度误差对协议参数估计过程的影响机制, 并基于发送端的三种现实假设, 提出相应数据优化方案, 以减轻源强度误差的负面影响. 同时, 综合考虑了源强度误差及有限码长效应, 以保障系统的现实安全性. 研究结果表明, 源强度误差不可忽视, 对于显著的强度波动, 系统的最大传输距离将减少约20 km. 因此, 在协议的实际实施过程中, 必须充分考虑源强度误差的影响, 并采取相应的措施来减少或消除这些误差. 本研究为现实条件下实施一维高斯调制连续变量量子密钥分发提供了理论依据, 为构建高效、低成本、小型化的量子通信网络探索了新方向.

关键词:

Abstract

Unidimensional Gaussian modulation continuous-variable quantum key distribution (UD CV-QKD) uses only one modulator to encode information. The UD CV-QKD has the advantages of low implementation cost and low random number consumption, making it attractive for the construction of future miniaturized and low-cost large-scale quantum communication networks. However, in the actual application of the protocol, the intensity fluctuation of the source pulsed light, device defects, and external environmental interference maybe lead to the generation of source intensity errors, thereby affecting the realistic security and performance of the protocol. To solve these problems, the security and performance of UD CV-QKD are studied in depth under source intensity errors in this work. The mechanism of source intensity errors influencing the protocol parameter estimation process is analyzed. To make it possible that the protocol can operate stably under various realistic conditions and ensure communication security, three practical assumptions about the sender’s abilities are made in this work, and corresponding data optimization processing schemes for these assumptions are proposed to reduce the negative influence of source intensity errors. Additionally, both source errors and finite-size effect are comprehensively considered to ensure the realistic security of the system. The simulation results indicate that the source intensity errors cannot be neglected and the maximum transmission distance of the system will be reduced by approximately 20 km for significant intensity fluctuations. Therefore, in the practical implementation of the protocol, the influence of source intensity errors must be fully considered, and the corresponding countermeasures should be taken to reduce or even eliminate these errors. This study provides theoretical guidance for securely implementing the UD CV-QKD in real-world environments.

Keywords:

continuous-variable quantum key distribution /
unidimensional modulation /
source errors /
realistic security

作者及机构信息

山西财经大学信息学院, 太原　030006

通信作者: 王普, wangpu@sxufe.edu.cn

基金项目: 国家自然科学基金(批准号: 62305198)和山西省自然科学基金(批准号: 202303021212168, 202103021224290)资助的课题.

Authors and contacts

School of Information, Shanxi University of Finance and Economics, Taiyuan 030006, China

Corresponding author: WANG Pu, wangpu@sxufe.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 62305198) and the Natural Science Foundation of Shanxi Province, China (Grant Nos. 202303021212168, 202103021224290).

文章全文

参考文献

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施引文献

图 1 一维高斯调制连续变量量子密钥分发模型　(a)准备测量方案; (b)基于纠缠方案

Fig. 1. Unidimensional Gaussian modulation continuous-variable quantum key distribution models: (a) Preparation and measurement scheme; (b) entanglement-based scheme.

下载: 全尺寸图片幻灯片

图 2 (a)实际的光脉冲强度$ I' $随时间$t$呈现出动态变化; (b)在相空间中, 由于源强度误差的影响, 实际制备的相干态可能会偏离目标相干态的位置

Fig. 2. (a) Actual optical pulse intensity dynamically changes over time; (b) the actual prepared coherent state may deviate from the target coherent state’s location in the phase space under the influence of source intensity errors.

下载: 全尺寸图片幻灯片

图 3 (a)不同均匀分布强度波动下密钥率随着传输距离的变化; (b)不同高斯分布强度波动下密钥率随着传输距离的变化

Fig. 3. (a) Comparison of secret key rates at various transmission distances for intensity fluctuation models following a uniform distribution; (b) comparison of secret key rates at various transmission distances for intensity fluctuation models adhering to a Gaussian distribution.

下载: 全尺寸图片幻灯片

图 4 不同源强度误差对协议性能的影响

Fig. 4. Influence of different source intensity errors on protocol performance.

下载: 全尺寸图片幻灯片

图 5 不同码长下协议性能比较　(a) 考虑第二种源误差模型; (b) 考虑第三种源误差模型

Fig. 5. Comparison of protocol performance under different total exchanged signals sizes: (a) Considering the second source error model; (b) considering the third source error model.

下载: 全尺寸图片幻灯片

图 6 $N = {10^{10}}$码长下不同源误差对应的协议密钥率和传输距离　(a) 考虑第二种源误差模型; (b) 考虑第三种源误差模型

Fig. 6. Protocol key rate and transmission distance corresponding to different source errors under the total exchanged signals of $N = {10^{10}}$: (a) Considering the second source error model; (b) considering the third source error model.

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

[1]	Bennett C H, Brassard G 1984 Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (Bangalore: IEEE) p175
[2]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[3]	Lo H K, Curty M, Tamaki K 2014 Nat. Photonics 8 595 Google Scholar
[4]	Bennett C H, Bessette F, Brassard G, Salvail L, Smolin J 1992 J. Cryptology 5 3 Google Scholar
[5]	Chen Y A, Zhang Q, Chen T Y, Cai W Q, Liao S K, Zhang J, Chen K, Yin J, Ren J G, Chen Z, Han S L, Yu Q, Liang K, Zhou F, Yuan X, Zhao M S, Wang T Y, Jiang X, Zhang L, Liu W Y, Li Y, Shen Q, Cao Y, Lu C Y, Shu R, Wang J Y, Li L, Liu N L, Xu F, Wang X B, Peng C Z, Pan J W 2021 Nature 589 214 Google Scholar
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[38]	Du S N, Wang P, Liu J Q, Tian Y, Li Y M 2023 Photonics Res. 11 463 Google Scholar
[39]	Wang X Y, Chen Z Y, Li Z H, Qi D K, Yu S, Guo H 2023 Opt. Lett. 48 3327 Google Scholar
[40]	Zhang M Q, Huang P, Wang P, Wei S R, Zeng G H 2023 Opt. Lett. 48 1184 Google Scholar
[41]	Hajomer A A E, Bruynsteen C, Derkach I, Jain N, Bomhals A, Bastiaens S, Andersen U L, Yin X, Gehring T 2024 Optica 11 1197 Google Scholar
[42]	Hajomer A A E, Derkach I, Filip R, Andersen U L, Usenko V C, Gehring T 2024 Light Sci. Appl. 13 291 Google Scholar
[43]	Ji F Y, Huang P, Wang T, Jiang X Q, Zeng G H 2024 Photonics Res. 12 1485 Google Scholar
[44]	Usenko V C, Grosshans F 2015 Phys. Rev. A 92 062337 Google Scholar
[45]	Wang P, Wang X Y, Li J Q, Li Y M 2017 Opt. Express 25 27995 Google Scholar
[46]	Wang X Y, Liu W Y, Wang P, Li Y M 2017 Phys. Rev. A 95 062330 Google Scholar
[47]	Jacobsen C S, Madsen L S, Usenko V C, Filip R, Andersen U L 2018 npj Quantum Inf. 4 32 Google Scholar
[48]	Liao Q, Guo Y, Xie C L, Huang D, Huang P, Zeng G H 2018 Quantum Inf. Process. 17 113 Google Scholar
[49]	Usenko V C 2018 Phys. Rev. A 98 032321 Google Scholar
[50]	Wang P, Wang X Y, Li Y M 2018 Entropy 20 157 Google Scholar
[51]	Wang X Y, Cao Y X, Wang P, Li Y M 2018 Quantum Inf. Process. 17 344 Google Scholar
[52]	Bai D Y, Huang P, Zhu Y Q, Ma H X, Xiao T L, Wang T, Zeng G H 2020 Quantum Inf. Process. 19 53 Google Scholar
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[55]	Zhao W, Shi R H, Feng Y Y, Huang D 2020 Phys. Lett. A 384 126061 Google Scholar
[56]	Zhou K L, Chen Z Y, Guo Y, Liao Q 2020 Phys. Lett. A 384 126074 Google Scholar
[57]	Bian Y M, Huang L Y, Zhang Y C 2021 Entropy 23 294 Google Scholar
[58]	Hu J K, Liao Q, Mao Y, Guo Y 2021 Quantum Inf. Process. 20 31 Google Scholar
[59]	Zhao W, Shi R H, Wu X M, Wang F Q, Ruan X C 2023 Opt. Express 31 17003 Google Scholar
[60]	Li Y Y, Wang T Y 2024 J. Phys. B: At. Mol. Opt. Phys. 57 145502 Google Scholar
[61]	Zhao R B, Zhou J, Shi R H, Shi J J 2024 Ann. Phys. 536 2300401 Google Scholar
[62]	Zheng Y, Huang P, Huang A Q, Peng J Y, Zeng G H 2019 Opt. Express 27 27369 Google Scholar
[63]	Zheng Y, Huang P, Huang A Q, Peng J Y, Zeng G H 2019 Phys. Rev. A 100 012313 Google Scholar
[64]	Wang P, Wang X Y, Li Y M 2020 Phys. Rev. A 102 022609 Google Scholar
[65]	Li C Y, Qian L, Lo H K 2021 npj Quantum Inf. 7 150 Google Scholar
[66]	Serafini A, Paris M G A, Illuminati F, Siena S D 2005 J. Opt. B: Quantum Semiclassical Opt. 7 R19 Google Scholar

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一维高斯调制连续变量量子密钥分发现实源强度误差的影响