title: Locally indistinguishable orthogonal product bases in arbitrary bipartite quantum system.
abstract: As we know, unextendible product basis (UPB) is an incomplete basis whose members cannot be perfectly distinguished by local operations and classical communication. However, very little is known about those incomplete and locally indistinguishable product bases that are not UPBs. In this paper, we first construct a series of orthogonal product bases that are completable but not locally distinguishable in a general m ⊗ n (m ≥ 3 and n ≥ 3) quantum system. In particular, we give so far the smallest number of locally indistinguishable states of a completable orthogonal product basis in arbitrary quantum systems. Furthermore, we construct a series of small and locally indistinguishable orthogonal product bases in m ⊗ n (m ≥ 3 and n ≥ 3). All the results lead to a better understanding of the structures of locally indistinguishable product bases in arbitrary bipartite quantum system.
authors: State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China.|College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China.
authors: Guang-Bao
authors: GB
authors: Xu
authors: State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China.|School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China.
authors: Ying-Hui
authors: YH
authors: Yang
authors: State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
authors: Qiao-Yan
authors: QY
authors: Wen
authors: State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
authors: Su-Juan
authors: SJ
authors: Qin
authors: State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China.
authors: Fei
authors: F
authors: Gao