基于线性光学元件的偏振-时间超纠缠W态浓缩

郭鹏亮; 席舜; 高成艳

doi:10.7498/aps.74.20241642

摘要

近年来, 量子通信得到快速的发展, 利用超纠缠态进行量子通信越来越广泛, 量子通信过程中大多使用的是最大超纠缠态, 而最大超纠缠态容易受到噪声的影响, 变成非最大超纠缠态, 将直接影响通信的质量. 因此, 本文提出利用线性光学元件对偏振-时间超纠缠W态浓缩的方案, 方案不需要借助辅助光子, 只需要用光学元件对接收的光子进行局部操作, 通过参数分裂法实现三光子偏振-时间超纠缠W态的浓缩, 此外方案还可以推广到N光子的超纠缠W态的浓缩. 本研究将为多方量子通信的远距离实现提供理论参考.

关键词:

Abstract

In recent years, quantum communication technology has developed rapidly, and quantum communication schemes based on hyperentangled states have attracted widespread attention due to their efficiency and security. However, in practical communication, maximally hyperentangled states are highly susceptible to environmental noise, which causes them to degrade into non-maximally hyperentangled states. This degradation significantly reduces the fidelity of the quantum information and communication efficiency. In this article, we propose an efficient entanglement concentration scheme to restore degraded polarization-time hyperentangled W states, thereby enhancing the reliability and transmission distance of multiparty quantum communication. The protocol employs the parameter-splitting approach, where the receiver performs local operations on received non-maximally hyperentangled photons by using linear optical elements, achieving hyperentanglement concentration through detector responses and post-selection. This method eliminates the need for auxiliary photons, thereby reducing the use of quantum resources and maintaining operational simplicity. Moreover, the scheme can be extended to N-photon hyperentangled W states. The theoretical calculations demonstrate that the success probability of the protocol is determined by the minimal parameter of the hyperentangled state, exhibiting a monotonic increase as this parameter grows. Under ideal conditions, the maximum success probability approaches unity and the success probability improves with the number of entangled photons increasing. When considering the efficiency of practical optical components, the maximal success probabilities for hyperentangled W states with N = 3, 4, and 5 are found to be 0.856, 0.791, and 0.732, respectively. Consequently, the proposed scheme efficiently concentrates the degraded polarization-time hyperentangled W state into the maximally hyperentangled state. This work is of significant importance for long-distance information transmission and provides theoretical references for implementing long-distance multi-party quantum communication.

Keywords:

作者及机构信息

1.
太原师范学院物理系, 晋中　030619

2.
太原师范学院计算与应用物理研究所, 晋中　030619

3.
太原师范学院计算机科学与技术学院, 晋中　030619

4.
太原师范学院, 智能优化计算与区块链技术山西省重点实验室, 晋中　030619

通信作者: 郭鹏亮, guopengliang@tynu.edu.cn

基金项目: 国家自然科学基金(批准号: 12305025)、山西省基础研究计划(批准号: 20210302124538, 202303021222218)和山西省高等学校科技创新项目(批准号: 2021L422, 2021L424)资助的课题.

Authors and contacts

1.
Department of Physics, Taiyuan Normal University, Jinzhong 030619, China

2.
Institute of Computational and Applied Physics, Taiyuan Normal University, Jinzhong 030619, China

3.
College of Computer Science and Technology, Taiyuan Normal University, Jinzhong 030619, China

4.
Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology, Taiyuan Normal University, Jinzhong 030619, China

Corresponding author: GUO Pengliang, guopengliang@tynu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12305025), the Fundamental Research Program of Shanxi Province, China (Grant Nos. 20210302124538, 202303021222218), and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (STIP), China (Grant Nos. 2021L422, 2021L424).

[1]	Barreiro J T, Langford N K, Peters N A, Kwiat P G 2005 Phys. Rev. Lett. 95 260501 Google Scholar
[2]	Gisin N, Thew R 2007 Nat. Photonics 1 165 Google Scholar
[3]	Liu W Q, Wei H R, Kwek L C 2020 Phys. Rev. Appl. 14 054057 Google Scholar
[4]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[5]	Liu X S, Long G L, Tong D M, Li F 2002 Phys. Rev. A 65 022304 Google Scholar
[6]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[7]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[8]	Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519 Google Scholar
[9]	Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12 Google Scholar
[10]	Sheng Y B, Zhou L, Long G L 2022 Sci. Bull. 67 367 Google Scholar
[11]	Zhou L, Sheng Y B 2022 Sci. China-Phys. Mech. Astron. 65 250311 Google Scholar
[12]	Ying J W, Zhao P, Zhong W, Du M M, Li X Y, Shen S T, Zhang A L, Zhou L, Sheng Y B 2024 Phys. Rev. Appl. 22 024040 Google Scholar
[13]	Zeng H, Du M M, Zhong W, Zhou L, Sheng Y B 2024 Fundam. Res. 4 851 Google Scholar
[14]	Hu X M, Guo Y, Liu B H, Li C F, Guo G C 2023 Nat. Rev. Phys. 5 339 Google Scholar
[15]	Wang X L, Cai X D, Su Z E, Chen M C, Wu D, Li L, Liu N L, Lu C Y, Pan J W 2015 Nature 518 516 Google Scholar
[16]	Graham T M, Bernstein H J, Wei T C, Junge M, Kwiat P G 2015 Nat. Commun. 6 7185 Google Scholar
[17]	Ren B C, Wang G Y, Deng F G 2015 Phys. Rev. A 91 032328 Google Scholar
[18]	Ren B C, Wei H R, Deng F G 2013 Laser. Phys. Lett. 10 095202 Google Scholar
[19]	任宝藏, 邓富国 2015 物理学报 64 160303 Google Scholar Ren B C, Deng F G 2015 Acta Phys. Sin. 64 160303 Google Scholar
[20]	Bennett C H, Bernstein H J, Popescu S, Schumacher B 1996 Phys. Rev. A 53 2046 Google Scholar
[21]	Zhao Z, Pan J W, Zhan M S 2001 Phys. Rev. A 64 014301 Google Scholar
[22]	Yamamoto T, Koashi M, Imoto N 2001 Phys. Rev. A 64 012304 Google Scholar
[23]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325 Google Scholar
[24]	Gu Y J, Xian L, Li W D, Ma L Z 2008 Chin. Phys Lett. 25 1191 Google Scholar
[25]	Zhou L, Sheng Y B, Zhao S M 2013 Chin. Phys. B 22 020307 Google Scholar
[26]	Guo R, Zhou L, Gu S P, Wang X F, Sheng Y B 2016 Chin. Phys. B 25 030302.Google Scholar
[27]	赵瑞通, 梁瑞生, 王发强 2017 物理学报 66 240301 Google Scholar Zhao R T, Liang R S, Wang F Q 2017 Acta Phys. Sin. 66 240301 Google Scholar
[28]	Zhou L, Wang D D, Wang X F, Gu S P, Sheng Y B 2017 Chin. Phys. B 26 020302 Google Scholar
[29]	Ren B C, Du F F, Deng F G 2013 Phys. Rev. A 88 012302 Google Scholar
[30]	Ren B C, Long G L 2015 Sci. Rep. 5 16444 Google Scholar
[31]	Li X H, Ghose S 2015 Phys. Rev. A 91 062302 Google Scholar
[32]	Cao C, Wang T J, Mi S C, Zhang R, Wang C 2016 Ann. Phys. 369 128 Google Scholar
[33]	Li C Y, Shen Y 2019 Opt. Express 27 13172 Google Scholar
[34]	Liu Q, Song G Z, Qiu T H, Zhang X M, Ma H Y, Zhang M 2020 Sci. Rep. 10 21444 Google Scholar
[35]	Jiang G L, Liu W Q, Wei H R 2023 Phys. Rev. Appl. 19 034044 Google Scholar
[36]	Shi X, Lu Y, Peng N, Rottwitt K, Ou H J 2022 J. Lightwave Technol. 40 7626 Google Scholar
[37]	Passos M H M, Balthazar W F, Khoury A Z, Hor-Meyll M, Davidovich L, Huguenin J A O 2018 Phys. Rev. A. 97 022321 Google Scholar
[38]	Kaneda F, Xu F, Chapman J, Kwiat P G 2017 Optica 4 1034 Google Scholar

施引文献

图 1 偏振-时间自由度的超纠缠W态的浓缩示意图 (PBS为偏振分束器, PC_L为普克尔斯盒, D_j为单光子探测器, D_L为延时装置, R_θj为波片, 下标j = A或B)

Fig. 1. Schematic diagram of the concentration of hyperentangled W states in polarization and time-bin degrees of freedom (PBS is the polarization beam splitter, PC_L is the Pockels Cells, D_j is the single photon detector, D_L denotes the time-delay device, and R_θj is the wave plate, where j = A or B)

下载: 全尺寸图片幻灯片

图 2 浓缩的成功概率P随系数a₃, b₃变化的示意图

Fig. 2. Schematic diagram of success probability P of entanglement concentration versus the coefficient a₃, b₃.

下载: 全尺寸图片幻灯片

图 3 浓缩的成功概率P与系数b_N(a_N)的关系示意图

Fig. 3. Schematic diagram of success probability P of entanglement concentration versus the coefficient b_N(a_N).

下载: 全尺寸图片幻灯片

[1]	Barreiro J T, Langford N K, Peters N A, Kwiat P G 2005 Phys. Rev. Lett. 95 260501 Google Scholar
[2]	Gisin N, Thew R 2007 Nat. Photonics 1 165 Google Scholar
[3]	Liu W Q, Wei H R, Kwek L C 2020 Phys. Rev. Appl. 14 054057 Google Scholar
[4]	Gisin N, Ribordy G, Tittel W, Zbinden H 2002 Rev. Mod. Phys. 74 145 Google Scholar
[5]	Liu X S, Long G L, Tong D M, Li F 2002 Phys. Rev. A 65 022304 Google Scholar
[6]	Long G L, Liu X S 2002 Phys. Rev. A 65 032302 Google Scholar
[7]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[8]	Zhu F, Zhang W, Sheng Y B, Huang Y D 2017 Sci. Bull. 62 1519 Google Scholar
[9]	Zhou L, Sheng Y B, Long G L 2020 Sci. Bull. 65 12 Google Scholar
[10]	Sheng Y B, Zhou L, Long G L 2022 Sci. Bull. 67 367 Google Scholar
[11]	Zhou L, Sheng Y B 2022 Sci. China-Phys. Mech. Astron. 65 250311 Google Scholar
[12]	Ying J W, Zhao P, Zhong W, Du M M, Li X Y, Shen S T, Zhang A L, Zhou L, Sheng Y B 2024 Phys. Rev. Appl. 22 024040 Google Scholar
[13]	Zeng H, Du M M, Zhong W, Zhou L, Sheng Y B 2024 Fundam. Res. 4 851 Google Scholar
[14]	Hu X M, Guo Y, Liu B H, Li C F, Guo G C 2023 Nat. Rev. Phys. 5 339 Google Scholar
[15]	Wang X L, Cai X D, Su Z E, Chen M C, Wu D, Li L, Liu N L, Lu C Y, Pan J W 2015 Nature 518 516 Google Scholar
[16]	Graham T M, Bernstein H J, Wei T C, Junge M, Kwiat P G 2015 Nat. Commun. 6 7185 Google Scholar
[17]	Ren B C, Wang G Y, Deng F G 2015 Phys. Rev. A 91 032328 Google Scholar
[18]	Ren B C, Wei H R, Deng F G 2013 Laser. Phys. Lett. 10 095202 Google Scholar
[19]	任宝藏, 邓富国 2015 物理学报 64 160303 Google Scholar Ren B C, Deng F G 2015 Acta Phys. Sin. 64 160303 Google Scholar
[20]	Bennett C H, Bernstein H J, Popescu S, Schumacher B 1996 Phys. Rev. A 53 2046 Google Scholar
[21]	Zhao Z, Pan J W, Zhan M S 2001 Phys. Rev. A 64 014301 Google Scholar
[22]	Yamamoto T, Koashi M, Imoto N 2001 Phys. Rev. A 64 012304 Google Scholar
[23]	Sheng Y B, Deng F G, Zhou H Y 2008 Phys. Rev. A 77 062325 Google Scholar
[24]	Gu Y J, Xian L, Li W D, Ma L Z 2008 Chin. Phys Lett. 25 1191 Google Scholar
[25]	Zhou L, Sheng Y B, Zhao S M 2013 Chin. Phys. B 22 020307 Google Scholar
[26]	Guo R, Zhou L, Gu S P, Wang X F, Sheng Y B 2016 Chin. Phys. B 25 030302.Google Scholar
[27]	赵瑞通, 梁瑞生, 王发强 2017 物理学报 66 240301 Google Scholar Zhao R T, Liang R S, Wang F Q 2017 Acta Phys. Sin. 66 240301 Google Scholar
[28]	Zhou L, Wang D D, Wang X F, Gu S P, Sheng Y B 2017 Chin. Phys. B 26 020302 Google Scholar
[29]	Ren B C, Du F F, Deng F G 2013 Phys. Rev. A 88 012302 Google Scholar
[30]	Ren B C, Long G L 2015 Sci. Rep. 5 16444 Google Scholar
[31]	Li X H, Ghose S 2015 Phys. Rev. A 91 062302 Google Scholar
[32]	Cao C, Wang T J, Mi S C, Zhang R, Wang C 2016 Ann. Phys. 369 128 Google Scholar
[33]	Li C Y, Shen Y 2019 Opt. Express 27 13172 Google Scholar
[34]	Liu Q, Song G Z, Qiu T H, Zhang X M, Ma H Y, Zhang M 2020 Sci. Rep. 10 21444 Google Scholar
[35]	Jiang G L, Liu W Q, Wei H R 2023 Phys. Rev. Appl. 19 034044 Google Scholar
[36]	Shi X, Lu Y, Peng N, Rottwitt K, Ou H J 2022 J. Lightwave Technol. 40 7626 Google Scholar
[37]	Passos M H M, Balthazar W F, Khoury A Z, Hor-Meyll M, Davidovich L, Huguenin J A O 2018 Phys. Rev. A. 97 022321 Google Scholar
[38]	Kaneda F, Xu F, Chapman J, Kwiat P G 2017 Optica 4 1034 Google Scholar

[1]	杨丽萍, 王纪平, 董莉, 修晓明, 计彦强. 基于超绝热技术快速制备里德伯超级原子W态. 物理学报, 2025, 74(10): 100305. doi: 10.7498/aps.74.20241694
[2]	刘圆凯, 侯云龙, 杨宜霖, 侯刘敏, 李渊华, 林佳, 陈险峰. 基于超纠缠的三用户全连接量子网络. 物理学报, 2025, 74(14): 140303. doi: 10.7498/aps.74.20250458
[3]	杨光, 刘琦, 聂敏, 刘原华, 张美玲. 基于极化-空间模超纠缠的量子网络多跳纠缠交换方法研究. 物理学报, 2022, 71(10): 100301. doi: 10.7498/aps.71.20212173
[4]	鹿博, 韩成银, 庄敏, 柯勇贯, 黄嘉豪, 李朝红. 超冷原子系综的非高斯纠缠态与精密测量. 物理学报, 2019, 68(4): 040306. doi: 10.7498/aps.68.20190147
[5]	何英秋, 丁东, 彭涛, 闫凤利, 高亭. 基于自发参量下转换源二阶激发过程产生四光子超纠缠态. 物理学报, 2018, 67(6): 060302. doi: 10.7498/aps.67.20172230
[6]	赵军龙, 张译丹, 杨名. 噪声对一种三粒子量子探针态的影响. 物理学报, 2018, 67(14): 140302. doi: 10.7498/aps.67.20180040
[7]	赵瑞通, 梁瑞生, 王发强. 电子自旋辅助实现光子偏振态的量子纠缠浓缩. 物理学报, 2017, 66(24): 240301. doi: 10.7498/aps.66.240301
[8]	任宝藏, 邓富国. 光子两自由度超并行量子计算与超纠缠态操控. 物理学报, 2015, 64(16): 160303. doi: 10.7498/aps.64.160303
[9]	丁东, 何英秋, 闫凤利, 高亭. 六光子超纠缠态制备方案. 物理学报, 2015, 64(16): 160301. doi: 10.7498/aps.64.160301
[10]	范榕华, 郭邦红, 郭建军, 张程贤, 张文杰, 杜戈. 基于轨道角动量的多自由度W态纠缠系统. 物理学报, 2015, 64(14): 140301. doi: 10.7498/aps.64.140301
[11]	张闻钊, 李文东, 史鹏, 顾永建. 3对非最大纠缠粒子的确定性纠缠浓缩协议. 物理学报, 2011, 60(6): 060303. doi: 10.7498/aps.60.060303
[12]	上官丽英, 孙洪祥, 陈秀波, 温巧燕, 朱甫臣. 三粒子纠缠W态隐形传态的正交完备基展开与算符变换. 物理学报, 2009, 58(3): 1371-1376. doi: 10.7498/aps.58.1371
[13]	冯发勇, 张强. 基于超纠缠交换的量子密钥分发. 物理学报, 2007, 56(4): 1924-1927. doi: 10.7498/aps.56.1924
[14]	周小清, 邬云文. 利用三粒子纠缠态建立量子隐形传态网络的探讨. 物理学报, 2007, 56(4): 1881-1887. doi: 10.7498/aps.56.1881
[15]	刘传龙, 郑亦庄. 纠缠相干态的量子隐形传态. 物理学报, 2006, 55(12): 6222-6228. doi: 10.7498/aps.55.6222
[16]	季玲玲, 吴令安. 光学超晶格中级联参量过程制备纠缠光子对. 物理学报, 2005, 54(2): 736-741. doi: 10.7498/aps.54.736
[17]	黄永畅, 刘敏. 一般WGHZ态和它的退纠缠与概率隐形传态. 物理学报, 2005, 54(10): 4517-4523. doi: 10.7498/aps.54.4517
[18]	郑亦庄, 戴玲玉, 郭光灿. 三粒子纠缠Ｗ态的隐形传态. 物理学报, 2003, 52(11): 2678-2682. doi: 10.7498/aps.52.2678
[19]	石名俊, 杜江峰, 朱栋培. 量子纯态的纠缠度. 物理学报, 2000, 49(5): 825-829. doi: 10.7498/aps.49.825
[20]	石名俊, 杜江峰, 朱栋培, 阮图南. 混合纠缠态的几何描述. 物理学报, 2000, 49(10): 1912-1918. doi: 10.7498/aps.49.1912

13-20241642Suppl.pdf

计量

文章访问数: 662
PDF下载量: 19
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板