Constructing the three-qudit unextendible product bases with strong nonlocality |
| |
| Affiliation: | 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 |
| |
| Abstract: | 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 ${{C}^{3}}otimes {{C}^{3}}otimes {{C}^{3}}$ 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 ${{C}^{d}}otimes {{C}^{d}}otimes {{C}^{d}}$ of size ${{left(d-1 right)}^{3}}+2d+5$, 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 ${{C}^{4}}otimes {{C}^{4}}otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}otimes {{C}^{3}}otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to the ${{C}^{{{d}_{1}}}}otimes {{C}^{{{d}_{2}}}}otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in by Halder et al. [$Phys. Rev. Lett$. 122 040403 (2019)], indicating that there do exist UPBs that can exhibit strong quantum nonlocality without entanglement. |
| |
| Keywords: | strong nonlocality unextendible product bases tri-tile structure construction method |
|
| 点击此处可从《中国物理 B》浏览原始摘要信息 |
|
点击此处可从《中国物理 B》下载免费的PDF全文 |
|
