Any<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>⊗</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math>subspace is locally distinguishable

Yu, Nengkun; Duan, Runyao; Ying, Mingsheng

doi:10.1103/physreva.84.012304

Cited by 60 publications

(31 citation statements)

References 13 publications

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“…M axim ally entangled states are o f considerable im portance in quantum inform ation theory and foundations o f quantum m echanics because o f their role in quantum com m unication prim itives such as quantum teleportation and superdense coding as w ell as dem onstrating m axim al violations o f Bell inequalities. Thus, studying the local distinguishability o f m axim ally entangled states is very m eaningful and has also attracted much attention [13][14][15][16][17][18][19][20][21][22][23][24][25][26], As is know n, d + 1 or m ore m axim ally entangled states in d ® d are not perfectly locally distinguishable [13][14][15]27], T herefore, one o f the main interesting questions is w hether a set o f N < d orthogonal m axim ally entangled states in d <g> d can be perfectly distinguished by local operations and classical com m unication (LO CC) for all d > 4.…”

Section: Introductionmentioning

confidence: 99%

Distinguishing maximally entangled states by one-way local operations and classical communication

et al. 2015

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In this paper, we mainly study the local indistinguishability of mutually orthogonal bipartite maximally entangled states. We construct sets of fewer than d orthogonal maximally entangled states which are not distinguished by one-way local operations and classical communication (LOCC) in the Hilbert space of d ® d. The proof, based on the Fourier transform of an additive group, is very simple but quite effective. Simultaneously, our results give a general unified upper bound for the minimum number of one-way LOCC indistinguishable maximally entangled states. This improves previous results which only showed sets of N > d -2 such states. Finally, our results also show that previous conjectures in Zhang et al.

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Section: Introductionmentioning

confidence: 99%

Distinguishing maximally entangled states by one-way local operations and classical communication

et al. 2015

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“…In general, it is well known that entanglement increases the difficulty of distinguishing orthogonal quantum states by LOCC [15][16][17][18][19][20][21][22]. However, many results reveal that entanglement is not necessary for LOCC indistinguishable quantum states.…”

Section: Introductionmentioning

confidence: 99%

Local indistinguishability of orthogonal product states

et al. 2016

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In the general bipartite quantum system m ⊗ n, Wang et al. [Y.-L Wang et al., Phys. Rev. A 92, 032313 (2015)] presented 3(m + n) − 9 orthogonal product states which cannot be distinguished by local operations and classical communication (LOCC). In this paper, we aim to construct less locally indistinguishable orthogonal product states in m ⊗ n. First, in 3 ⊗ n(3 < n) quantum system, we construct 3n − 2 locally indistinguishable orthogonal product states which are not unextendible product bases. Then, for m ⊗ n(4 ≤ m ≤ n), we present 3n + m − 4 orthogonal product states which cannot be perfectly distinguished by LOCC. Finally, in the general bipartite quantum system m ⊗ n(3 ≤ m ≤ n), we show a smaller set with 2n − 1 orthogonal product states and prove that these states are LOCC indistinguishable using a very simple but quite effective method. All of the above results demonstrate the phenomenon of nonlocality without entanglement.

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“…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 . 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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Any2⊗nsubspace is locally distinguishable

Cited by 60 publications

References 13 publications

Distinguishing maximally entangled states by one-way local operations and classical communication

Distinguishing maximally entangled states by one-way local operations and classical communication

Local indistinguishability of orthogonal product states

LOCC indistinguishable orthogonal product quantum states

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