利用弱Hardy型悖论与Hardy-Bell不等式检验Bell非局域性  

Detecting Bell nonlocality based on weak Hardy-like paradoxes and Hardy-Bell inequalities

作　　者：韩看远 郭志华[1] 曹怀信[1] 汤卫东 HAN KanYuan;GUO ZhiHua;CAO HuaiXin;TANG WeiDong(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《中国科学：物理学、力学、天文学》2024年第7期158-173,共16页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:11871318,12271325);陕西省高层次人才特支计划(编号:1503070117)资助项目。

摘　　要：Bell非局域性是最为特殊的量子非局域性,也是量子信息处理的重要资源.检验Bell非局域性通常有两类方法:Bell不等式方法与全对无(All-versus-Nothing,AvN)证明.后者包括GHZ论述和Hardy悖论方法.本文通过构建弱Hardy型悖论和Hardy-Bell不等式,以及Hardy不等式,提出了检验关联张量与量子态的Bell非局域性的新方法.首先,建立了弱Hardy型悖论(WHLP),并获得了三体关联张量的Hardy-Bell不等式(HBI).基于已有的n比特纯态的Hardy不等式,证明了n比特Bell局域关联张量的Hardy不等式.其次,建立了基于条件概率的三体系统的WHLP和HBI.从理论和实验角度来看,我们构建的WHLP比通常的Hardy型悖论更容易构建,因此在检验Bell非局域性方面更加有效.Bell nonlocality is a special quantum nonlocality and has emerged as an important resource in quantum information pro-cessing tasks.Typically,there are two types of strategies for testing the Bell nonlocality:the Bell inequality method and the“all-versus-nothing proof”,the later includes methods such as the GHZ argument and Hardy paradox.The objective of this work is to provide new methods for detecting Bell nonlocality by understanding Hardy-like paradoxes(HLPs)and Hardy-Bell inequalities(HBIs)as well as Hardy inequality.First,the weak HLP(WHLP)is established,and an HBI is obtained for tripartite correlation tensors(CTs)with two inputs and two outcomes.Based on an existing Hardy inequality for an n-qubit pure state,a Hardy inequality is proven for n-partite Bell local CTs.Second,the WHLP and HBI are proven for tripartite states in terms of conditional probabilities.Our WHLP is theoretically and practically easier to construct and more efficient in checking Bell nonlocality compared to the usual HLP.

关 键 词：关联张量 Bell非局域性 弱Hardy型悖论 Hardy-Bell不等式 Hardy不等式 

分 类 号：O413[理学—理论物理]