高维系统中混合量子态的不可扩展乘积基

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 563-569.

高维系统中混合量子态的不可扩展乘积基

韩琦^*(),韩娅楠(),白宁,寇亚欣

西北师范大学数学与统计学院兰州 730070

收稿日期:2021-07-28 修回日期:2022-09-02 出版日期:2023-04-26 发布日期:2023-04-17
通讯作者: 韩琦，E-mail: hanqi1978@nwnu.edu.cn
作者简介:韩娅楠，E-mail: 13993113263@139.com
基金资助:
国家自然科学基金(62261049);国家自然科学基金(12261080);甘肃省自然科学基金(20JR10RA085);甘肃省教育厅高等教育创新基金(2022A-017)

Unextendible Product Bases of Mixed Quantum States in Higher Dimensional Systems

Han Qi(),Han Yanan(),Bai Ning,Kou Yaxin

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070

Received:2021-07-28 Revised:2022-09-02 Online:2023-04-26 Published:2023-04-17
Supported by:
National Natural Science Foundation of China(62261049);National Natural Science Foundation of China(12261080);Natural Science Foundation of Gansu Province(20JR10RA085);Higher Education Innovation Fund of Gansu Provincial Department of Education(2022A-017)

摘要/Abstract

摘要：

在量子信息理论的背景下, 正映射 St?rmer-Woronowicz 特征仅适用于低维 Hilbert 空间, 因此对于高维 Hilbert 空间, 混合量子态的局部正转置(PPT)不会构成可分性的充要条件, 故存在 PPT 纠缠态. 束缚纠缠是量子纠缠的一种弱形式, 它在局部运算和经典通讯下无法提纯任何纠缠, 这意味着不是任何纠缠都能直接运用到量子通信中. 如何刻画束缚纠缠态, 是量子信息中的核心问题之一, 而利用不可扩展乘积基可以构造束缚纠缠态[21]. 该文给出了高维系统中混合量子态的不可扩展乘积基的一种构造, 并给出此基中包含基向量个数的规律.

关键词: 正映射, 局部正转置, 可分准则, 不可扩展乘积基, 纠缠态

Abstract:

In the context of quantum information theory, the positive mapping St?rmer-Woronowicz feature is only applicable to low dimensions, the positive partial transposition (PPT) of the mixed quantum state does not form a necessary and sufficient condition for separability in a higher dimensional Hilbert space, so PPT entanglement states exists. Bound entanglement is a weak form of quantum entanglement. It cannot purify any entanglement under local operation and classical communication, which means that not all entanglement can be directly applied to quantum communication. How to characterize bound entanglement states is one of the key problems in quantum information. Bound entanglement states can be constructed by means of an unexpandable product basis. In this paper, we give a constructon of unextensible product basis for mixed quantum states in high dimensional systems, and give the rule of the number of basis vectors in this basis.

Key words: Positive map, Positive partial transposition, Separability criterion, Unextensible product basis, Entanglement state

中图分类号:

O211.9

韩琦, 韩娅楠, 白宁, 寇亚欣. 高维系统中混合量子态的不可扩展乘积基[J]. 数学物理学报, 2023, 43(2): 563-569.

Han Qi, Han Yanan, Bai Ning, Kou Yaxin. Unextendible Product Bases of Mixed Quantum States in Higher Dimensional Systems[J]. Acta mathematica scientia,Series A, 2023, 43(2): 563-569.

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