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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.
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Keywords:
- continuous variable quantum key distribution /
- Bayesian parameter estimation method /
- monkey algorithm /
- dynamic polarization controller
[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 492Google Scholar
[2] Ren S Y, Wang Y, Su X L 2022 Sci. China Inform. Sci. 65 200502Google 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 180507Google Scholar
[4] Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145Google Scholar
[5] Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902Google Scholar
[6] Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature 421 238Google 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 042305Google Scholar
[8] Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378Google 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 621Google Scholar
[10] 刘建强, 王旭阳, 白增量, 李永民 2016 65 100303Google Scholar
Liu J Q, Wang X Y, Bai Z L, Li Y M 2016 Acta Phys. Sin. 65 100303Google Scholar
[11] Huang D, Huang P, Li H S, Wang T, Zhou Y M, Zeng G H 2016 Opt. Lett. 41 3511Google 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 040303Google 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 035006Google Scholar
[14] Xu F H, Ma X F, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002Google Scholar
[15] 钟海, 叶炜, 吴晓东, 郭迎 2021 70 020301Google Scholar
Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301Google Scholar
[16] 刘金璐, 杨杰, 张涛, 樊矾, 黄伟, 徐兵杰 2021 70 240303Google Scholar
Liu J L, Yang J, Zhang T, Fan F, Huang W, Xu B J 2021 Acta Phys. Sin. 70 240303Google Scholar
[17] 廖骎, 柳海杰, 王铮, 朱凌瑾 2023 72 040301Google Scholar
Liao Q, Liu H J, Wang Z, Zhu L J 2023 Acta Phys. Sin. 72 040301Google Scholar
[18] Liu W Y, Cao Y X, Wang X Y, Li Y M 2020 Phys. Rev. A 102 032625Google Scholar
[19] Noé R, Heidrich H, Hoffmann D 1988 Opt. Lett. 13 527Google Scholar
[20] Koch B, Hidayat A, Zhang H B, Mirvoda V, Lichtinger M, Sandel D, Noé R 2008 IEEE Photon. Technol. Lett. 20 961Google 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 210Google 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 210Google 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 2314002Google Scholar
You Y, Qi Y F, Shen H, Zou X X, He B, Zhou J 2020 Acta Opt. Sin. 40 2314002Google Scholar
[26] 张启业, 朱勇, 苏洋, 周华, 经继松 2013 光学学报 33 0506001Google Scholar
Zhang Q Y, Zhu Y, Su Y, Zhou H, Jing J S 2013 Acta Opt. Sin. 33 0506001Google Scholar
[27] Xavier G B, Walenta N, Faria G V D, Temporão G P, Gisin N, Zbinden H, Weid J P V D 2009 New J. Phys. 11 045015Google Scholar
[28] Chen J, Wu G, Xu L, Gu X, Wu E, Zeng H 2009 New J. Phys. 11 065004Google Scholar
[29] Li D D, Gao S, Li G C, Xue L, Wang L W, Lu C B, Xiang Y, Zhao Z Y, Yan L C, Chen Z Y, Yu G, Liu J H 2018 Opt. Express 26 22793Google Scholar
[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 27923Google 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 71 130306Google 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 130306Google 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 350Google Scholar
[34] Mekhtiev E E, Gerasin I S, Rudavin N V, Duplinsky A V, Kurochkin Y V 2021 J. Phys. Conf. Ser. 2086 012092Google Scholar
[35] Wang T, Huang P, Wang S Y, Zeng G H 2019 Opt. Express 27 26689Google Scholar
[36] Zhou M S, Li Y Q, Xiang Z H, Swoboda G, Cen Z Z 2007 Tsinghua Sci. Technol. 12 546Google Scholar
[37] Jin B T 2008 Int. J. Numer. Meth. Eng. 76 230Google Scholar
[38] CappÉ O, Godsill S J, Moulines E 2007 Proc. IEEE 95 899Google Scholar
[39] An M J 2012 Geophys. J. Int. 191 849Google Scholar
[40] Fox E P 1998 Technometrics 40 155
[41] Schönfeld P 1989 Statistical Papers 30 212Google Scholar
[42] Toussaint U V 2011 Rev. Mod. Phys. 83 943Google Scholar
[43] Barker A L, Brown D E, Martin W N 1995 Comput. Math. Appl. 30 55Google Scholar
[44] Cohn S E 1997 J. Meteor. Soc. Jpn. 75 257Google Scholar
[45] Zhuang L F, Pan F, Ding F 2012 Appl. Math. Model. 36 3454Google Scholar
[46] Ying M S 2010 Artif. Intell. 174 162Google Scholar
[47] Lamata L, Sanz M, Solano E 2019 Adv. Quantum Technol. 2 1900075Google Scholar
[48] Liu D, Pei C X, Quan D X, Zhao N 2010 Chin. Phys. Lett. 27 050306Google Scholar
[49] Li X H, Zhou P, Liang Y J, Li C Y, Zhou H Y, Deng F G 2006 Chin. Phys. Lett. 23 1080Google Scholar
[50] Haykin S 2005 IEEE J. Sel. Area. Comm. 23 201Google Scholar
[51] Corsi F, Galtarossa A, Palmieri L 1998 J. Lightw. Technol. 16 1832Google Scholar
[52] Galtarossa A, Schiano M, Someda C G, Daino B, Matera F, Zaninello R, Bergamin F 1991 Electron. Lett. 27 595Google 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 19Google 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 413Google 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 1173Google Scholar
Zhang X G, Duan G Y, Xi L X 2009 Acta Opt. Sin. 29 1173Google Scholar
[61] Franceschetti G, Smith C P 1981 J. Opt. Soc. Am. 71 1487Google Scholar
[62] Baptista M S 1998 Phys. Lett. A 240 50Google 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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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.
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[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 492Google Scholar
[2] Ren S Y, Wang Y, Su X L 2022 Sci. China Inform. Sci. 65 200502Google 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 180507Google Scholar
[4] Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145Google Scholar
[5] Grosshans F, Grangier P 2002 Phys. Rev. Lett. 88 057902Google Scholar
[6] Grosshans F, Assche G V, Wenger J, Brouri R, Cerf N J, Grangier P 2003 Nature 421 238Google 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 042305Google Scholar
[8] Jouguet P, Kunz-Jacques S, Leverrier A, Grangier P, Diamanti E 2013 Nat. Photonics 7 378Google 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 621Google Scholar
[10] 刘建强, 王旭阳, 白增量, 李永民 2016 65 100303Google Scholar
Liu J Q, Wang X Y, Bai Z L, Li Y M 2016 Acta Phys. Sin. 65 100303Google Scholar
[11] Huang D, Huang P, Li H S, Wang T, Zhou Y M, Zeng G H 2016 Opt. Lett. 41 3511Google 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 040303Google 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 035006Google Scholar
[14] Xu F H, Ma X F, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002Google Scholar
[15] 钟海, 叶炜, 吴晓东, 郭迎 2021 70 020301Google Scholar
Zhong H, Ye W, Wu X D, Guo Y 2021 Acta Phys. Sin. 70 020301Google Scholar
[16] 刘金璐, 杨杰, 张涛, 樊矾, 黄伟, 徐兵杰 2021 70 240303Google Scholar
Liu J L, Yang J, Zhang T, Fan F, Huang W, Xu B J 2021 Acta Phys. Sin. 70 240303Google Scholar
[17] 廖骎, 柳海杰, 王铮, 朱凌瑾 2023 72 040301Google Scholar
Liao Q, Liu H J, Wang Z, Zhu L J 2023 Acta Phys. Sin. 72 040301Google Scholar
[18] Liu W Y, Cao Y X, Wang X Y, Li Y M 2020 Phys. Rev. A 102 032625Google Scholar
[19] Noé R, Heidrich H, Hoffmann D 1988 Opt. Lett. 13 527Google Scholar
[20] Koch B, Hidayat A, Zhang H B, Mirvoda V, Lichtinger M, Sandel D, Noé R 2008 IEEE Photon. Technol. Lett. 20 961Google 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 210Google 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 210Google 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 2314002Google Scholar
You Y, Qi Y F, Shen H, Zou X X, He B, Zhou J 2020 Acta Opt. Sin. 40 2314002Google Scholar
[26] 张启业, 朱勇, 苏洋, 周华, 经继松 2013 光学学报 33 0506001Google Scholar
Zhang Q Y, Zhu Y, Su Y, Zhou H, Jing J S 2013 Acta Opt. Sin. 33 0506001Google Scholar
[27] Xavier G B, Walenta N, Faria G V D, Temporão G P, Gisin N, Zbinden H, Weid J P V D 2009 New J. Phys. 11 045015Google Scholar
[28] Chen J, Wu G, Xu L, Gu X, Wu E, Zeng H 2009 New J. Phys. 11 065004Google Scholar
[29] Li D D, Gao S, Li G C, Xue L, Wang L W, Lu C B, Xiang Y, Zhao Z Y, Yan L C, Chen Z Y, Yu G, Liu J H 2018 Opt. Express 26 22793Google Scholar
[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 27923Google 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 71 130306Google 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 130306Google 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 350Google Scholar
[34] Mekhtiev E E, Gerasin I S, Rudavin N V, Duplinsky A V, Kurochkin Y V 2021 J. Phys. Conf. Ser. 2086 012092Google Scholar
[35] Wang T, Huang P, Wang S Y, Zeng G H 2019 Opt. Express 27 26689Google Scholar
[36] Zhou M S, Li Y Q, Xiang Z H, Swoboda G, Cen Z Z 2007 Tsinghua Sci. Technol. 12 546Google Scholar
[37] Jin B T 2008 Int. J. Numer. Meth. Eng. 76 230Google Scholar
[38] CappÉ O, Godsill S J, Moulines E 2007 Proc. IEEE 95 899Google Scholar
[39] An M J 2012 Geophys. J. Int. 191 849Google Scholar
[40] Fox E P 1998 Technometrics 40 155
[41] Schönfeld P 1989 Statistical Papers 30 212Google Scholar
[42] Toussaint U V 2011 Rev. Mod. Phys. 83 943Google Scholar
[43] Barker A L, Brown D E, Martin W N 1995 Comput. Math. Appl. 30 55Google Scholar
[44] Cohn S E 1997 J. Meteor. Soc. Jpn. 75 257Google Scholar
[45] Zhuang L F, Pan F, Ding F 2012 Appl. Math. Model. 36 3454Google Scholar
[46] Ying M S 2010 Artif. Intell. 174 162Google Scholar
[47] Lamata L, Sanz M, Solano E 2019 Adv. Quantum Technol. 2 1900075Google Scholar
[48] Liu D, Pei C X, Quan D X, Zhao N 2010 Chin. Phys. Lett. 27 050306Google Scholar
[49] Li X H, Zhou P, Liang Y J, Li C Y, Zhou H Y, Deng F G 2006 Chin. Phys. Lett. 23 1080Google Scholar
[50] Haykin S 2005 IEEE J. Sel. Area. Comm. 23 201Google Scholar
[51] Corsi F, Galtarossa A, Palmieri L 1998 J. Lightw. Technol. 16 1832Google Scholar
[52] Galtarossa A, Schiano M, Someda C G, Daino B, Matera F, Zaninello R, Bergamin F 1991 Electron. Lett. 27 595Google 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 19Google 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 413Google 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 1173Google Scholar
Zhang X G, Duan G Y, Xi L X 2009 Acta Opt. Sin. 29 1173Google Scholar
[61] Franceschetti G, Smith C P 1981 J. Opt. Soc. Am. 71 1487Google Scholar
[62] Baptista M S 1998 Phys. Lett. A 240 50Google 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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