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arXiv 2009.02555quant-ph
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纠缠交换理论及其扩展

Entanglement swapping theory and beyond

Key Laboratory of Aerospace Information Security and Trusted Computing, Ministry of Education, School of Cyber Science and Engineering, Wuhan University(教育部空天信息安全与可信计算重点实验室,武汉大学计算机学院)

Zhaoxu Ji, Huanguo Zhang

AI总结:

本文提出了一种新的纠缠交换理论,涵盖了纯态、混合态以及纠缠交换链的分析,并提供了新的证明方法。

摘要:

我们专注于纠缠交换的一般理论,包括纯态和混合态的纠缠交换。我们还研究了纠缠交换链的理论,可以视为纠缠交换的应用。对于最大纠缠态,我们考虑了不将每个子系统限制在同一基底下的2级最大纠缠态的纠缠交换。我们进一步考虑了d级最大纠缠态之间的纠缠交换,这通过在包含所选纠缠态的第一个粒子和不涉及第一个粒子的其他纠缠态的粒子上进行联合测量来实现。对于一般纯态的纠缠交换,我们将双部分一般纯态的情况推广到多态情况。此外,我们提出了双部分一般纯态与最大纠缠态之间的纠缠交换。对于纠缠交换链,我们提出了最大纠缠态的纠缠交换链,通过在每个状态的多个粒子上进行联合测量来实现,我们使用数学归纳法证明了最大纠缠态和一般纯态的纠缠交换链的结果。此外,我们研究了混合态的纠缠交换和纠缠交换链,包括X态和混合最大纠缠态。最后,我们为之前的工作[2022, Physica A, 585, 126400]提供了一个新的证明。

英文摘要:

We focus on the general theory of entanglement swapping, including entanglement swapping of pure and mixed states. We also study the theory of entangled swapping chains, which can be regarded as an application of entangled swapping. For maximally entangled states, we consider the entanglement swapping of 2-level maximally entangled states without limiting each subsystem to be in the same basis. We further consider the entanglement swapping between d-level maximally entangled states, which is realized by performing a joint measurement on the particles that contain the first particle of the selected entangled states and the particles without involving the first particle in other entangled states. For the entanglement swapping of general pure state, we generalize the case of two bipartite general pure states to multi-state cases. Besides, we propose the entanglement swapping between bipartite general pure states and maximally entangled states. For entanglement swapping chains, we propose the entanglement swapping chains for maximally entangled states, which is realized by performing joint measurements on multiple particles in each state, we use mathematical induction to prove the results of entanglement swapping chains of maximally entangled states and that of general pure states. Moreover, we study the entanglement swapping and entanglement swapping chains of mixed states, including X states and mixed maximally entangled states. Finally, we provide a new proof for our previous work [2022, Physica A, 585, 126400].

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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