Persistency of tripartite nonlocality sharing with noise

Zhao Lin-Yang; He Kan; Zhang Yan-Fang

doi:10.7498/aps.73.20241150

Abstract

Recently, researchers have proven that an infinite number of Charlies and a pair of Alice and Bob can share standard tripartite nonlocality and genuinely nonsignal nonlocality by violating the Mermin and NS inequalities within tripartite systems. This discovery undoubtedly provides new perspectives and potential in quantum information science. However, it should be noted that the above-mentioned conclusion is derived on the highly idealized assumption that the quantum system is perfect and free from external disturbances. In reality, the realization of this ideal state is a challenging proposition. As a fundamental aspect of quantum mechanics, the phenomenon of quantum entanglement is susceptible to the influence of external factors, such as noise, during its practical implementation. Additionally, the process of quantum measurement can introduce potential errors, which may potentially diminish or even negate the observed quantum nonlocality. In light of the above situation, we investigate whether it is possible to share the corresponding quantum nonlocality, despite the inevitable occurrence of noise and error. This paper aims to study and discuss the persistency of nonlocality in noisy three-qubit systems. Firstly, the sufficient conditions are provided for Alice and Bob to share standard tripartite nonlocality with any number of Charlies, even when measurements are noisy and the initial three-qubit system is in a maximally entangled state with noise. This finding indicates that certain standard tripartite nonlocality can persist under non-ideal conditions as long as certain conditions are met. Moreover, this article elucidates the necessary conditions for multiple independent Charlies to share genuinely nonsignal nonlocality with a pair of Alice and Bob in a non-ideal state. This implies that despite the presence of noise and errors, this type of genuinely nonsignal nonlocality can still be securely shared among multiple parties as long as specific conditions are met. This research provides a new theoretical basis for the security and feasibility of quantum communication. The comprehensive analysis presented in this paper offers insights into the behavior of triple quantum nonlocality under noiseless conditions.

Keywords:

Authors and contacts

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Corresponding author: He Kan, hekanquantum@163.com ; Zhang Yan-Fang, zhangyanfang@tyut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12271394).

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References

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图 1 共享三体量子非局域场景

Figure 1. Scenario of sharing the genuine tripartite nonlocality.

DownLoad: Full-Size Img PowerPoint

[1]	Bell J S 1964 Phys. Phys. Fiz. 1 195 Google Scholar
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[3]	Acín A, Brunner N, Gisin N, Massar S, Pironio S, Scarani V 2007 Phys. Rev. Lett. 98 230501 Google Scholar
[4]	Li J J, Wang Y, Li H W, Bao W S 2020 Chin. Phys. B 29 030303 Google Scholar
[5]	周贤韬, 江英华 2023 物理学报 72 020302 Google Scholar Zhou X T, Jiang Y H 2023 Acta Phys. Sin. 72 020302 Google Scholar
[6]	张沛, 周小清, 李智伟 2014 物理学报 63 130301 Google Scholar Zhao P, Zhou X Q, Li Z W 2014 Acta Phys. Sin. 63 130301 Google Scholar
[7]	Dynes J F, Yuan Z L, Sharpe A W, Shields A J 2008 Appl. Phys. Lett. 93 031109 Google Scholar
[8]	Acín A, Masanes L 2016 Nature 540 213 Google Scholar
[9]	Curchod F J, Johansson M, Augusiak R, Hoban M J, Wittek P, Acín A 2017 Phys. Rev. A 95 020102 Google Scholar
[10]	Colbeck R, Renner R 2012 Nat. Phys. 8 450 Google Scholar
[11]	Colbeck R, Kent A 2011 J. Phys. A: Math. Theor. 44 095305 Google Scholar
[12]	李宏欣, 王相宾, 刘欣, 韩宇, 闫宝, 王伟 2017 现代物理 7 257 Google Scholar Li H X, Wang X B, Liu X, Han Y, Yan B, Wang W 2017 Modern Physics 7 257 Google Scholar
[13]	杜聪, 王金东, 秦晓娟, 魏正军, 於亚飞, 张智明 2020 物理学报 69 190301 Google Scholar Du C, Wang J D, Qin X J, Wei Z J, Yu Y F, Zhang Z M 2020 Acta Phys. Sin. 69 190301 Google Scholar
[14]	东晨, 赵尚弘, 董毅, 赵卫虎, 赵静 2014 物理学报 63 170303 Google Scholar Dong C, Zhao S H, Dong Y, Zhao W H, Zhao J 2014 Acta Phys. Sin. 63 170303 Google Scholar
[15]	Silva R, Gisin N, Guryanova Y, Popescu S 2015 Phys. Rev. Lett. 114 250401 Google Scholar
[16]	Mal S, Majumdar A, Home D 2016 Mathematics 4 48 Google Scholar
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[19]	Brown P J, Colbeck R 2020 Phys. Rev. Lett. 125 090401 Google Scholar
[20]	Zhang T G, Fei S M 2021 Phys. Rev. A 103 032216 Google Scholar
[21]	Mermin N D 1990 Phys. Rev. Lett. 65 1838 Google Scholar
[22]	Saha S, Das D, Sasmal S, Sarkar D, Mukherjee K, Roy K, Bhattacharya S S 2019 Quantum Inf. Process. 18 42 Google Scholar
[23]	Svetlichny G 1987 Phys. Rev. D 35 3066 Google Scholar
[24]	Bancal J D, Barrett J, Gisin N, Pironio S 2013 Phys. Rev. A 88 014102 Google Scholar
[25]	Xi Y, Li M S, Fu L B, Zheng Z J 2023 Phys. Rev. A 107 062419 Google Scholar
[26]	Mukherjee K, Chakrabarty I, Mylavarapu G 2023 Phys. Rev. A 107 032404 Google Scholar
[27]	Mukherjee K 2022 Phys. Rev. A 106 042206 Google Scholar
[28]	Ralston J P, Jain P, Nodland B 1998 Phys. Rev. Lett. 81 26 Google Scholar
[29]	Pearle P M 1970 Phys. Rev. D 2 1418 Google Scholar
[30]	Yang S S, Hou J C, He K 2024 Chin. Phys. B 33 010302 Google Scholar

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