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 siz...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.展开更多
基金supported by the National Key R&D Program of China(Grant No.2020YFB1805405)the 111 Project(Grant No.B21049)+1 种基金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)。
文摘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.
