Research on dynamic polarization control in continuous variable quantum key distribution systems

Zhang Guang-Wei; Bai Jian-Dong; Jie Qi; Jin Jing-Jing; Zhang Yong-Mei; Liu Wen-Yuan

doi:10.7498/aps.73.20231890

Abstract

In a commercial fiber-based quantum key distribution system, the local and signal optical fields are transmitted through long distance fibers by using time division multiplexing and polarization multiplexing. The state of polarization of the optical field is inevitably disturbed by random birefringence of the standard single-mode fiber caused by external complex environments. This drift of the state of polarization significantly affects the balanced homodyne detection results and the secret key rate. Therefore, the key technology of the dynamic polarization control unit is crucial for the system in a large-scale commercial application. We theoretically analyze and prove that the polarization control unit only needs the combination of two degrees of freedom when considering the result of an arbitrary polarization extinction ratio at the receiver of the system. To overcome the influence of polarization variations, we propose a chaotic monkey algorithm based on Bayesian parameter estimation method and implement intelligence algorithm on field programmable gate array (FPGA) hardware under pulsed light with an integral-type detector for the dynamic polarization control unit. The simulation results show that the optimal combination is four degrees of freedom and the optimal prior distribution is an exponential distribution among various distributions in the dynamic polarization control unit. According to the simulation results, the experimental results show that the achieved polarization extinction ratio is over 30 dB and the average time of polarization control is 400 μs for a single random polarization scrambling. By combining the dynamic polarization control unit with the system, we demonstrate the continuous variable quantum key distribution (CV-QKD) under a continuous polarization scrambling scope of 0－2 krad/s and verify its effectiveness. In addition, the methods presented will improve the performance of the system and expand the range of applications even under strong external disturbance.

Keywords:

Authors and contacts

Department of Physics, School of Semiconductor and Physics, North University of China, Taiyuan 030051, China

Corresponding author: Liu Wen-Yuan, liuweny@nuc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12104419, 12104417, 12104418) and the Basic Research Program of Shanxi Province, China (Grant Nos. 20210302124689, 20210302124161, 20210302124025).

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References

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Cited By

图 1 挤压型电控偏振控制器

Figure 1. Extrusion type electronically polarization controller.

DownLoad: Full-Size Img PowerPoint

图 2 调节挤压器延迟量偏振态的变化轨迹　(a) 固定${0^{{\circ }}}$挤压器, 调节${45^{{\circ }}}$挤压器相位延迟量; (b) 调节${0^{{\circ }}}$和${45^{{\circ }}}$挤压器相位延迟量

Figure 2. Change trajectory of state of polarization when adjusting phase retardation of extruder: (a) Fixing ${0^{{\circ }}}$ extruder, adjusting phase retardation of the ${45^{{\circ }}}$ extruder; (b) adjusting phase retardation of the ${0^{{\circ }}}$ and ${45^{{\circ }}}$ extruders.

DownLoad: Full-Size Img PowerPoint

图 3 贝叶斯-混沌猴群算法流程图

Figure 3. Program flow diagram of Bayesian-chaotic monkey algorithm.

DownLoad: Full-Size Img PowerPoint

图 4 先验分布类型和偏振自由度达到目标偏振态所需迭代次数

Figure 4. Average number of iterations to achieve target state of polarization based on prior distribution and degrees of freedom of polarization.

DownLoad: Full-Size Img PowerPoint

图 5 动态偏振控制单元示意图

Figure 5. Schematic diagram of the dynamic polarization control unit.

DownLoad: Full-Size Img PowerPoint

图 6 控制目标偏振态迭代次数统计分布

Figure 6. Statistical distribution of iterations to achieve target of state of polarization.

DownLoad: Full-Size Img PowerPoint

图 7 单次偏振控制过程中消光比与时间关系

Figure 7. Observed polarization extinction ratio versus the time for a typical single random polarization control process.

DownLoad: Full-Size Img PowerPoint

图 8 连续偏振扰动速率对系统关键参数影响　(a) 通道传输效率; (b) 额外噪声

Figure 8. Influence of continuous polarization scrambling on key parameters of the system: (a) Channel transmittance; (b) excess noise.

DownLoad: Full-Size Img PowerPoint

[1]	Tian Y, Wang P, Liu J Q, Du S N, Liu W Y, Lu Z G, Wang X Y, Li Y M 2022 Optica 9 492 Google Scholar
[2]	Ren S Y, Wang Y, Su X L 2022 Sci. China Inform. Sci. 65 200502 Google Scholar
[3]	Ma L, Yang J, Zhang T, Shao Y, Liu J L, Luo Y J, Wang H, Huang W, Fan F, Zhou C, Zhang L L, Zhang S, Zhang Y C, Li Y, Xu B J 2023 Sci. China Inform. Sci. 66 180507 Google Scholar
[4]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[5]	Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902 Google Scholar
[6]	Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature 421 238 Google Scholar
[7]	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
[8]	Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378 Google Scholar
[9]	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
[10]	刘建强, 王旭阳, 白增量, 李永民 2016 物理学报 65 100303 Google Scholar Liu J Q, Wang X Y, Bai Z L, Li Y M 2016 Acta Phys. Sin. 65 100303 Google Scholar
[11]	Huang D, Huang P, Li H S, Wang T, Zhou Y M, Zeng G H 2016 Opt. Lett. 41 3511 Google Scholar
[12]	Li Y M, Wang X Y, Bai Z L, Liu W Y, Yang S S, Peng K C 2017 Chin. Phys. B 26 040303 Google Scholar
[13]	Zhang Y C, Li Z Y, Chen Z Y, Weedbrook C, Zhao Y J, Wang X Y, Huang Y D, Xu C C, Zhang X X, Wang Z Y, Li M, Zhang X Y, Zheng Z Y, Chu B J, Gao X Y, Meng N, Cai W W, Wang Z, Wang G, Yu S, Guo H 2019 Quantum Sci. Technol. 4 035006 Google Scholar
[14]	Xu F H, Ma X F, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
[15]	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
[16]	刘金璐, 杨杰, 张涛, 樊矾, 黄伟, 徐兵杰 2021 物理学报 70 240303 Google Scholar Liu J L, Yang J, Zhang T, Fan F, Huang W, Xu B J 2021 Acta Phys. Sin. 70 240303 Google Scholar
[17]	廖骎, 柳海杰, 王铮, 朱凌瑾 2023 物理学报 72 040301 Google Scholar Liao Q, Liu H J, Wang Z, Zhu L J 2023 Acta Phys. Sin. 72 040301 Google Scholar
[18]	Liu W Y, Cao Y X, Wang X Y, Li Y M 2020 Phys. Rev. A 102 032625 Google Scholar
[19]	Noé R, Heidrich H, Hoffmann D 1988 Opt. Lett. 13 527 Google Scholar
[20]	Koch B, Hidayat A, Zhang H B, Mirvoda V, Lichtinger M, Sandel D, Noé R 2008 IEEE Photon. Technol. Lett. 20 961 Google Scholar
[21]	李伟文, 章献民, 陈抗生, 邹英寅 2005 光子学报 34 820 Li W W, Zhang X M, Chen K S, Zou Y Y 2005 Acta Photon. Sin. 34 820
[22]	刘尉悦, 曹蕾, 陈厦微, 张亮, 李扬, 曹原, 任继刚, 蔡文奇, 廖胜凯, 彭承志 2016 红外与毫米波学报 35 210 Google Scholar Liu W Y, Cao L, Chen X W, Zhang L, Li Y, Cao Y, Ren J G, Cai W Q, Liao S K, Peng C Z 2016 J. Infrared Millim. Waves 35 210 Google Scholar
[23]	李伟文, 金晓峰, 章献民, 陈抗生 2006 浙江大学学报:工学版 40 443 Li W W, Jin X F, Zhang X M, Chen K S 2006 J. Zhejiang Univ. (Eng. Sci.) 40 443
[24]	Zhu J J, Zhang X G, Duan G Y, Wang Q G 2006 Semi. Photon. Tech. 12 217
[25]	尤阳, 漆云凤, 沈辉, 邹星星, 何兵, 周军 2020 光学学报 40 2314002 Google Scholar You Y, Qi Y F, Shen H, Zou X X, He B, Zhou J 2020 Acta Opt. Sin. 40 2314002 Google Scholar
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[28]	Chen J, Wu G, Xu L, Gu X, Wu E, Zeng H 2009 New J. Phys. 11 065004 Google Scholar
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[30]	Ding Y Y, Chen H, Wang S, He D Y, Yin Z Q, Chen W, Zhou Z, Guo G C, Han Z F 2017 Opt. Express 25 27923 Google Scholar
[31]	曹若琳, 彭清轩, 王金东, 陈勇杰, 黄云飞, 於亚飞, 魏正军, 张智明 2022 物理学报 71 130306 Google Scholar Cao R L, Peng Q X, Wang J D, Chen Y J, Huang Y F, Yu Y F, Wei Z J, Zhang Z M 2022 Acta Phys. Sin. 71 130306 Google Scholar
[32]	周琦, 苏成志, 马万卓 2022 激光杂志 43 32 Zhou Q, Su C Z, Ma W Z 2022 Laser J. 43 32
[33]	Muga N J, Ramos M F, Mantey S T, Silva N A, Pinto A N 2020 IET Optoelectron. 14 350 Google Scholar
[34]	Mekhtiev E E, Gerasin I S, Rudavin N V, Duplinsky A V, Kurochkin Y V 2021 J. Phys. Conf. Ser. 2086 012092 Google Scholar
[35]	Wang T, Huang P, Wang S Y, Zeng G H 2019 Opt. Express 27 26689 Google Scholar
[36]	Zhou M S, Li Y Q, Xiang Z H, Swoboda G, Cen Z Z 2007 Tsinghua Sci. Technol. 12 546 Google Scholar
[37]	Jin B T 2008 Int. J. Numer. Meth. Eng. 76 230 Google Scholar
[38]	CappÉ O, Godsill S J, Moulines E 2007 Proc. IEEE 95 899 Google Scholar
[39]	An M J 2012 Geophys. J. Int. 191 849 Google Scholar
[40]	Fox E P 1998 Technometrics 40 155
[41]	Schönfeld P 1989 Statistical Papers 30 212 Google Scholar
[42]	Toussaint U V 2011 Rev. Mod. Phys. 83 943 Google Scholar
[43]	Barker A L, Brown D E, Martin W N 1995 Comput. Math. Appl. 30 55 Google Scholar
[44]	Cohn S E 1997 J. Meteor. Soc. Jpn. 75 257 Google Scholar
[45]	Zhuang L F, Pan F, Ding F 2012 Appl. Math. Model. 36 3454 Google Scholar
[46]	Ying M S 2010 Artif. Intell. 174 162 Google Scholar
[47]	Lamata L, Sanz M, Solano E 2019 Adv. Quantum Technol. 2 1900075 Google Scholar
[48]	Liu D, Pei C X, Quan D X, Zhao N 2010 Chin. Phys. Lett. 27 050306 Google Scholar
[49]	Li X H, Zhou P, Liang Y J, Li C Y, Zhou H Y, Deng F G 2006 Chin. Phys. Lett. 23 1080 Google Scholar
[50]	Haykin S 2005 IEEE J. Sel. Area. Comm. 23 201 Google Scholar
[51]	Corsi F, Galtarossa A, Palmieri L 1998 J. Lightw. Technol. 16 1832 Google Scholar
[52]	Galtarossa A, Schiano M, Someda C G, Daino B, Matera F, Zaninello R, Bergamin F 1991 Electron. Lett. 27 595 Google Scholar
[53]	谢晓新, 徐森禄 1990 陕西师大学报(自然科学版) 18 82 Xie X X, Xu S L 1990 J. Shaanxi Normal Univ. (Nat. Sci. Ed.) 18 82
[54]	Xu X P, Zhang D J 2018 Comput. Eng. Appl. 54 144
[55]	Zhao R Q, Tang W S 2008 J. Uncertain Syst. 2 165
[56]	Alfaro M E, Holder M T 2006 Annu. Rev. Ecol. Evol. Syst. 37 19 Google Scholar
[57]	Dempster A P, Laird N M, Rubin D B 1977 J. R. Stat. Soc. Series B 39 1
[58]	Reimherr M, Meng X L, Nicolae D L 2021 J. R. Stat. Soc. Series B 83 413 Google Scholar
[59]	张晓光, 席丽霞, 崔楠, 张虎, 肖晓晟, 唐先锋 2023 光纤通信系统中的偏振光学 (北京: 清华大学出版社) 第18—36页 Zhang X G, Xi L X, Cui N, Zhang H, Xiao X S, Tang X F 2023 Polarization Optics in Optical Fiber Communication (Beijing: Tsinghua University Press) pp18–36
[60]	张晓光, 段高燕, 席丽霞 2009 光学学报 29 1173 Google Scholar Zhang X G, Duan G Y, Xi L X 2009 Acta Opt. Sin. 29 1173 Google Scholar
[61]	Franceschetti G, Smith C P 1981 J. Opt. Soc. Am. 71 1487 Google Scholar
[62]	Baptista M S 1998 Phys. Lett. A 240 50 Google Scholar
[63]	安毓英, 曾晓东, 冯喆珺 2010 光电探测与信号处理 (北京: 科学出版社) 第172—180页 An Y Y, Zeng X D, Feng Z J 2010 Photoelectric Detection and Signal Processing (Beijing: Science Press) pp172–180

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Vol. 73, Issue 6 - 2024-03-20

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