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).

文章全文

参考文献

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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

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基于线性光学元件的偏振-时间超纠缠W态浓缩