数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 366-376.
• 研究论文 • 上一篇
噪声环境下星型量子网络的非局域性共享
刘姗, 贺衎, 张峰*(
)
- 太原理工大学数学学院 山西晋中 030600
-
收稿日期:2024-12-20修回日期:2025-04-24出版日期:2026-02-26发布日期:2026-01-19 -
通讯作者:张峰 E-mail:zhangfeng.0631@163.com -
基金资助:国家自然科学基金(12271394);山西省回国留学基金(2020-031);山西省基础研究项目(202203021212211)
Sharing Quantum Nonlocality in Noisy Star Networks
Shan Liu, Kan He, Feng Zhang*()
- College of Mathematics, Taiyuan University of Technology, Shanxi Jinzhong 030600
-
Received:2024-12-20Revised:2025-04-24Online:2026-02-26Published:2026-01-19 -
Contact:Feng Zhang E-mail:zhangfeng.0631@163.com -
Supported by:NSFC(12271394);Shanxi Scholarship Council of China(2020-031);Fundamental Research Program of Shanxi Province(202203021212211)
摘要：
量子系统的贝尔非局域性共享是量子力学中的一个基本特征, 而网络量子态的非局域性共享能力比贝尔非局域性更强, 网络量子态的结构也更加复杂. 在实际应用中, 量子纠缠生成的误差和量子执行测量的过程中的噪声会导致非局域性共享的衰减. 该文探讨了星型网络中单边和多边测量下含噪声的非局域性共享持续存在的充分条件, 并分析了不同噪声条件对星型网络非局域性共享持续性的影响. 该文还探讨了双局域场景, 这一场景可以被看作是一种特殊的星型网络场景.
中图分类号:
- O177
引用本文
刘姗, 贺衎, 张峰. 噪声环境下星型量子网络的非局域性共享[J]. 数学物理学报, 2026, 46(1): 366-376.
Shan Liu, Kan He, Feng Zhang. Sharing Quantum Nonlocality in Noisy Star Networks[J]. Acta mathematica scientia,Series A, 2026, 46(1): 366-376.
图1
顺序非局域性共享. Alice 与 Bob 最初共享的双量子比特态为 $\rho _{AB}^{\left( 1 \right)}$, Alice 执行 POVM 并产生一个输出, 随后将所得的态传递给 Alice$_{2}$. Alice$_{2}$ 接收该态后继续执行 POVM. 继续这一过程, 直到 Alice$_{m}$ 和 Bob 之间共享测后态 $\rho _{AB}^{\left( m \right)}$."
图2
星型网络场景. $n$ 个独立的源 S$_{1}$, S$_{2}$, $\cdots$, S$_{k}$, $\cdots$, S$_{n}$ 分别向每个节点 Alice, A$_2$, $\cdots$, A$_k$, $\cdots$, A$_n$ 和中心节点 Bob 分布纠缠双量子比特态 $\rho_{A_1B}$, $\rho_{A_2B}$, $\cdots$, $\rho_{A_kB}$, $\cdots$, $\rho_{A_nB}$."
图3
星型网络场景中单边测量下的非局域性共享. Alice 一侧进行顺序测量, Alice$ _m $ 和 Bob 之间共享的态变为 $ \rho _{A_1B}^{\left( m \right)} $, 此时网络态由 $ \rho _{AB}^{\left( 1 \right)}\otimes \rho _{A_2B}\otimes \cdots\otimes \rho _{A_nB} $ 变为 $ \rho _{AB}^{\left( m \right)}\otimes \rho _{A_2B}\otimes \cdots\otimes \rho _{A_nB} $."
图4
(a) $ n=2 $ 时蓝色, 橙色, 绿色分别代表满足 $ \gamma _1\left( \alpha,\theta \right) \in \left( 0,1 \right) $, $ \gamma _2\left( \alpha,\theta \right) \in \left( 0,1 \right) $, $ \gamma _3\left( \alpha,\theta \right) \in \left( 0,1 \right) $ 的参数 $ \alpha $ 和$ \theta $ 的范围. (b) $ n=3 $. (c) $ n=10 $. (d) $ n=30 $. (e) $ n=2 $ 时与单个 Bob 共享噪声初始态的非局域性的最大 Alice 的数量 $ n_{A}^{\max} $ 与参数 $ \alpha $ 的关系. (f) $ n=3 $. (g) $ n=10 $. (h) $ n=30 $."
图5
(a) $ n=2 $ 时蓝色, 橙色, 绿色分别代表满足 $ \gamma _1\left( \delta,\theta \right) \in \left( 0,1 \right) $, $ \gamma _2\left( \delta,\theta \right) \in \left( 0,1 \right) $, $ \gamma _3\left( \delta,\theta \right) \in \left( 0,1 \right) $ 的参数 $ \alpha $ 和 $ \theta $ 的范围. (b) $ n=3 $. (c) $ n=10 $. (d) $ n=30 $. (e) $ n=2 $ 时与单个 Bob 共享噪声初始态的非局域性的最大 Alice 的数量 $ n_{A}^{\max} $ 与参数 $ \delta $ 的关系. (f) $ n=3 $. (g) $ n=10 $. (h) $ n=30 $."
图6
星型网络场景中多边测量下的非局域性共享. Alice$ _1 $, A$ _2 $, $ \cdots $, A$ _p $ 一侧进行顺序测量, 此时网络态由 $ \rho _{A_1B}\otimes \rho _{A_2B}\otimes \cdots\otimes \rho _{A_nB} $ 变为 $ \rho _{A_1B}^{\left( m \right)}\otimes \rho _{A_2B}^{\left( m \right)}\otimes \cdots\otimes \rho _{A_pB}^{\left( m \right)}\otimes \cdots\otimes \rho _{A_nB} $."
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