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.
journal_name
Sci Repjournal_title
Scientific reportsauthors
Zhang X,Tan X,Weng J,Li Ydoi
10.1038/srep28864subject
Has Abstractpub_date
2016-07-05 00:00:00pages
28864issn
2045-2322pii
srep28864journal_volume
6pub_type
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