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量子纠缠的单配性OA北大核心CSTPCD

Monogamy of quantum entanglement

中文摘要英文摘要

与宏观物理世界不同,量子世界粒子之间的关联性作为物理资源其关联的强弱不可以任意分配.比如3 量子比特 A、B、C,若 A与B处于极大纠缠态,则 A与C之间不再有纠缠,把这一性质称为单配性.这一性质也是量子信息能够实现安全保密通信的原因之一.自 2000 年Coff-man、Kundu和Wootters(CKW)首次给出纠缠单配性的数学定义以来,学者对这一性质进行了大量研究.基于此,该文系统地对目前研究结果进行梳理,主要对2018 年给出的纠缠单配性新定义以及2019 年基于新定义所得到的结论进行总结,并对量子关联度量多配性新定义及基于新定义得到的辅助纠缠的多配性讨论进行总结.结果表明,新定义对于研究单配性和多配性关系更加便捷,单配性关系取决于约化函数是否为严格凹函数,而辅助纠缠都满足多配性关系.研究结果为今后研究量子关联提供了新思路.

In contrast with the classical world,quantum correlations used as physical resource can not be freely shared.For example,if qubit A is maximally entangled with qubit B,then it must be uncorrelated(not even classically)with qubit C.This feature of quantum corretation is termed monogamy.Such a monogamy property is of fundamental importance since it guarantees the security in quantum information communication.Ever since the monogamy relation was quantified for the first time in the seminal paper by Coffman,Kundu,and Wootters(CKW)in 2000 for three qubits,it has been studied intensively in more general settings in the last two decades.All the related results so far are reviewed.Especially,our new definition of monogamy in 2018 and the results based on which we obtained in 2019 are introduced.In addition,the new definition of polygamy relation for measure of quantum correlation and the polygamy relation of the entanglement of assistance are reviewed.Consequently,it is found that our improved definitions of monogamy and polygamy can reveal the distributions of entanglement and the entanglement of assistance more effectively,and that the monogamy of entanglement closely depends on the strict concavity of the reduced function,all the assisted entanglement of entanglement monotones are shown to be polygamous.Our method will shed new light on the studying of the quantum correlations.

郭钰

内蒙古大学数学科学学院,内蒙古呼和浩特 010021

数学

量子系统;纠缠;纠缠度量;单配性;约化函数;辅助纠缠;多配性

quantum system;entanglement;entanglement measure;monogamy;reduced function;assisted entanglement;polygamy

《陕西师范大学学报(自然科学版)》 2024 (002)

57-79 / 23

国家自然科学基金(11971277);内蒙古大学高层次人才科研启动项目(10000-23112101/049);山西省 2022 年度留学人员科技活动择优资助项目(20220031)

10.15983/j.cnki.jsnu.2024001

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