Constructing the three-qudit unextendible product bases with strong nonlocality  

作　　者：Bichen Che Zhao Dou Xiubo Chen Yu Yang Jian Li Yixian Yang 车碧琛;窦钊;陈秀波;杨榆;李剑;杨义先(Information Security Center,State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China;Information Security Center,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]Information Security Center,State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China [2]Information Security Center,Beijing University of Posts and Telecommunications,Beijing 100876,China

出　　处：《Chinese Physics B》2022年第6期170-182,共13页中国物理B（英文版）

基　　金：supported by the National Key R&D Program of China(Grant No.2020YFB1805405);the 111 Project(Grant No.B21049);the Foundation of Guizhou Provincial Key Laboratory of Public Big Data(Grant No.2019BDKFJJ014);the Fundamental Research Funds for the Central Universities(Grant Nos.2019XD-A02 and 2020RC38)。

摘　　要：Unextendible product bases(UPBs)are interesting members of a family of orthogonal product bases.Here,we investigate the construction of 3-qudit UPBs with strong nonlocality.First,a UPB set in C^(3)■C^(3)■C^(3)of size 19 is presented based on the shift UPBs.By mapping the system to a Rubik’s cube,we provide a general method of constructing UPBs in C^(d)■C^(d)■C^(d)of size(d-1)^(3)+2d+5,whose corresponding Rubik’s cube is composed of four parts.Second,for the more general case where the dimensions of parties are different,we extend the classical tile structure to the 3-qudit system and propose the tri-tile structure.By means of this structure,a C^(4)■C^(4)■C^(5)system of size 38 is obtained based on a C^(3)■C^(3)■C^(4)system of size 19.Then,we generalize this approach to the C^(d1)■C^(d2)■C^(d3)system which also consists of four parts.Our research provides a positive answer to the open question raised in by Halder et al.[Phys.Rev.Lett.122040403(2019)],indicating that there do exist UPBs that can exhibit strong quantum nonlocality without entanglement.

关 键 词：strong nonlocality unextendible product bases tri-tile structure construction method 

分 类 号：O413[理学—理论物理]