两体系统真隐非局域正交直积态集合的构造  

Constructions of orthogonal product state sets with genuine hidden nonlocality in bipartite system

作　　者：张青[1,2] 左会娟 ZHANG Qing;ZUO Hui-Juan(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;School of Cyberspace Security,Hebei University of Engineering Science,Shijiazhuang 050091,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China;Hebei International Joint Research Center for Mathematics and Interdisciplinary Science,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024 [2]河北工程技术学院网络空间安全学院,石家庄050091 [3]河北省计算数学与应用重点实验室,石家庄050024 [4]河北省数学与交叉科学国际联合研究中心,石家庄050024

出　　处：《中国科学:物理学、力学、天文学》2025年第4期100-107,共8页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：石家庄市驻冀高校基础研究项目(编号:241790697A);河北师范大学交叉学科研究基金(编号:L2025J01);国家自然科学基金(编号:62272208);河北省自然科学基金(编号:A2023205045)资助。

摘　　要：对于一个局域可区分且局域无冗余的正交量子态集合,如果存在一个保正交的局域测量,使得测后态集合是局域不可区分的,则称该集合具有真隐非局域性.若测后态集合的基数等于原集合的基数,则称原集合具有类型I真隐非局域性;否则,称原集合具有类型Ⅱ真隐非局域性.本文主要研究具有真隐非局域性的正交直积态集合的构造问题,得到以下结果:在两体系统C^(d1)⊗C^(d2)(d_(1)>8,d_(2)>10,且d_(1),d_(2)为偶数)上构造了类型Ⅰ真隐非局域正交直积态集合;在两体系统C^(d)⊗C^(2d)(d>3)上构造了类型Ⅱ真隐非局域正交直积态集合.特别地,我们找到了C^(3)⊗C^(6)上类型Ⅱ真隐非局域正交直积态集合,此时系统的局域维数最小.A set of orthogonal quantum states has genuine hidden nonlocality,if there is an orthogonality preserving local measurement such that the locally distinguishable and locally redundant set become locally indistinguishable under it.If the cardinality of the postmeasurement sets is equal to the cardinality of the original set,then we say the original set has genuine hidden nonlocality of type Ⅰ;otherwise,we say it has genuine hidden nonlocality of type Ⅱ.In this study,we mainly study the constructions of orthogonal product state sets with genuine hidden nonlocality,and the main results are as follows.We first construct a product set with genuine hidden nonlocality of type Ⅰ in C^(d1)⊗C^(d2)(d_(1)>8,d_(2)>10,di is even).In addition,we present a type-Ⅱ genuine hidden nonlocal set without entanglement in C^(d)⊗C^(2d)(d>3).In particular,we found the product state set with genuine hidden nonlocality of type Ⅱ in C^(3)⊗C^(6),which has the smallest local dimension.

关 键 词：非局域性 真隐非局域性 局域冗余 直积态 

分 类 号：O413.1[理学—理论物理] O413[理学—物理]