Positive-partial-transpose distinguishability for lattice-type maximally entangled states

Xiong, Zong-Xing; Li, Maosheng; Zheng, Zhu-Jun; Zhu, Changjiang; Fei, Shao-Ming

doi:10.1103/physreva.99.032346

Cited by 9 publications

(2 citation statements)

References 18 publications

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“…Here we present an incomplete list of the results about the local distinguishability of maximally entangled states [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and product states [2,. Another direction of related research is to study how much resource of entanglement are needed in order to distinguish quantum states which are locally indistinguishable [44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Local distinguishability based genuinely quantum nonlocality without entanglement

Li¹,

Wang²,

Shi³

et al. 2021

J. Phys. A: Math. Theor.

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Recently, Halder et al (2019 Phys. Rev. Lett. 122 040403) proposed the concept of strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of its subsystems. Due to the complexity of the problem, most results are limited to tripartite systems. Here we consider a weaker form of nonlocality which is called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for every bipartition of the subsystems. In this work, we study how to construct sets of orthogonal product states which are genuinely nonlocal. Firstly, we present a set of product states with simple structure in bipartite systems that is locally indistinguishable. After that, based on a simple observation, we present a general method to construct genuinely nonlocal sets of multipartite product states by using those sets that are genuinely nonlocal but with less parties. As a consequence, we obtain that genuinely nonlocal sets of fully product states exist in any L parties systems provided L ⩾ 3 and d i ⩾ 3 for all i.

show abstract

Section: Introductionmentioning

confidence: 99%

Local distinguishability based genuinely quantum nonlocality without entanglement

Li¹,

Wang²,

Shi³

et al. 2021

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The maximally entangled states and the product states, as being two extreme sets among the pure states, their local distinguishability is the most attractive. Here we present an incomplete list of the results about the local distinguishability of maximally entangled states [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and product states [2,. Another direction of related research is to study how much resource of entanglement are needed in order to distinguish quantum states which are locally indistinguishable [44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Local distinguishability based genuinely quantum nonlocality without entanglement

Li,

Wang,

Shi

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

Recently, Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition of the subsystems. As the difficulty of the problem, most of the results are restricted to tripartite systems. Here we consider a weaker form of nonlocality called local distinguishability based genuine nonlocality. A set of orthogonal multipartite quantum states is said to be genuinely nonlocal if it is locally indistinguishable for every bipartition of the subsystems. In this work, we tend to study the latter form of nonlocality. First, we present an elegant set of product states in bipartite systems that is locally indistinguishable. After that, based on a simple observation, we present a general method to construct genuinely nonlocal sets of multipartite product states by using those sets that are genuinely nonlocal but with less parties. As a consequence, we obtain that genuinely nonlocal sets of fully product states exist for all possible multipartite quantum systems.

show abstract

Small set of orthogonal product states with nonlocality

Wang

Chen

2022

Quantum Inf Process

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Positive-partial-transpose distinguishability for lattice-type maximally entangled states

Cited by 9 publications

References 18 publications

Local distinguishability based genuinely quantum nonlocality without entanglement

Local distinguishability based genuinely quantum nonlocality without entanglement

Local distinguishability based genuinely quantum nonlocality without entanglement

Small set of orthogonal product states with nonlocality

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