title: LOCC indistinguishable orthogonal product quantum states.
abstract: We construct two families of orthogonal product quantum states that cannot be exactly distinguished by local operation and classical communication (LOCC) in the quantum system of (2k+i) ⊗ (2l+j) (i, j ∈ {0, 1} and i ≥ j ) and (3k+i) ⊗ (3l+j) (i, j ∈ {0, 1, 2}). And we also give the tiling structure of these two families of quantum product states where the quantum states are unextendible in the first family but are extendible in the second family. Our construction in the quantum system of (3k+i) ⊗ (3l+j) is more generalized than the other construction such as Wang et al.'s construction and Zhang et al.'s construction, because it contains the quantum system of not only (2k) ⊗ (2l) and (2k+1) ⊗ (2l) but also (2k) ⊗ (2l+1) and (2k+1) ⊗ (2l+1). We calculate the non-commutativity to quantify the quantumness of a quantum ensemble for judging the local indistinguishability. We give a general method to judge the indistinguishability of orthogonal product states for our two constructions in this paper. We also extend the dimension of the quantum system of (2k) ⊗ (2l) in Wang et al.'s paper. Our work is a necessary complement to understand the phenomenon of quantum nonlocality without entanglement.
authors.affiliation: Department of Mathematics, Jinan University, Guangzhou, P.R. China.
authors.forename: Xiaoqian
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, Jinan University, Guangzhou, P.R. China.
authors.forename: Xiaoqing
authors.initials: X
authors.lastname: Tan
authors.affiliation: Department of Computer Science, Jinan University, Guangzhou, P.R. China.
authors.forename: Jian
authors.initials: J
authors.lastname: Weng
authors.affiliation: School of Computer Science and Engineering, South China University of Technology, Guangzhou, P.R. China.
authors.forename: Yongjun
authors.initials: Y
authors.lastname: Li