Local indistinguishability of orthogonal product states

Zhang, Zhichao; Gao, Fei; Cao, Ya; Qin, Su‐Juan; Wen, Qiaoyan

doi:10.1103/physreva.93.012314

Cited by 81 publications

(33 citation statements)

References 44 publications

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“…Lemma. In C m ⊗ C n (3 ≤ m ≤ n), there are 2n − 1 LOCC indistinguishable orthogonal product states [23]. Next, we give another set of product states which look much more concise than the ones in lemma for C m ⊗ C n (4 ≤ m ≤ n).…”

Section: Constructions Of Even Partite Casementioning

confidence: 99%

The local indistinguishability of multipartite product states

Wang

Zheng

et al. 2016

Quantum Inf Process

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In this paper, we mainly study the local indistinguishability of multipartite product states. Firstly, we follow the method of Z.-C. Zhang et al [Phys. Rev. A 93, 012314(2016)] to give another more concise set of 2n−1 orthogonal product states in C m ⊗C n (4 ≤ m ≤ n) which can not be distinguished by local operations and classical communication(LOCC). Then we use the 3 dimension cubes to present some product states which give us an intuitive view how to construct locally indistinguishable product states in tripartite quantum system. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite system.

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Section: Constructions Of Even Partite Casementioning

confidence: 99%

The local indistinguishability of multipartite product states

Wang

Zheng

et al. 2016

Quantum Inf Process

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“…For example, it is impossible, by LOCC, to transform a product state into an entangled state 4 , even with a nonzero probability. When global operators cannot be implemented by LOCC, it reflects the fundamental feature of quantum mechanics which is called nonlocality and has received wide attention in recent years 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 . A fundamental result in this area was the discovery by Bennett et al 22 of a complete orthogonal product basis which cannot be distinguished perfectly by LOCC.…”

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confidence: 99%

Entanglement as a resource to distinguish orthogonal product states

Zhang

Gao

Cao

et al. 2016

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It is known that there are many sets of orthogonal product states which cannot be distinguished perfectly by local operations and classical communication (LOCC). However, these discussions have left the following open question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In m ⊗ n, certain classes of unextendible product bases (UPB) which can be distinguished perfectly using entanglement as a resource, had been presented in 2008. In this paper, we present protocols which use entanglement more efficiently than teleportation to distinguish some classes of orthogonal product states in m ⊗ n, which are not UPB. For the open question, our results offer rather general insight into why entanglement is useful for such tasks, and present a better understanding of the relationship between entanglement and nonlocality.

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“…The study of quantum nonlocality is one of the fundamental problems in quantum information theory. LOCC is usually used to verify whether quantum states are perfectly distinguished 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 or not. In refs 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , they focus on the local distinguishability of quantum states such as multipartite orthogonal product states can be exactly distinguished 10 or how to distinguish two quantum pure states 11 12 .…”

mentioning

confidence: 99%

“…In refs 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , they focus on the local distinguishability of quantum states such as multipartite orthogonal product states can be exactly distinguished 10 or how to distinguish two quantum pure states 11 12 . Moreover, locally indistinguishability 13 14 15 16 17 18 19 20 21 22 23 of quantum orthogonal product states plays an important role in exploring quantum nonlocality.…”

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confidence: 99%

LOCC indistinguishable orthogonal product quantum states

Zhang

Tan

Weng

et al. 2016

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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.

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Local indistinguishability of orthogonal product states

Cited by 81 publications

References 44 publications

The local indistinguishability of multipartite product states

The local indistinguishability of multipartite product states

Entanglement as a resource to distinguish orthogonal product states

LOCC indistinguishable orthogonal product quantum states

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