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

作者机构：Information Security CenterState Key Laboratory of Networking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijing 100876China Information Security CenterBeijing University of Posts and TelecommunicationsBeijing 100876China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2022年第31卷第6期

页      面：170-182页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

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) 

主　　题：strong nonlocality unextendible product bases tri-tile structure construction method 

摘      要：Unextendible product bases(UPBs)are interesting members of a family of orthogonal product ***,we investigate the construction of 3-qudit UPBs with strong ***,a UPB set in C^(3)■C^(3)■C^(3)of size 19 is presented based on the shift *** 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 ***,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 *** 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 ***,we generalize this approach to the C^(d1)■C^(d2)■C^(d3)system which also consists of four *** research provides a positive answer to the open question raised in by Halder et al.[***.122040403(2019)],indicating that there do exist UPBs that can exhibit strong quantum nonlocality without entanglement.