Entanglement as a resource to distinguish orthogonal product states

Zhang, Zhichao; Gao, Fei; Cao, Tian-Qing; Qin, Su‐Juan; Wen, Qiaoyan

doi:10.1038/srep30493

Cited by 37 publications

(22 citation statements)

References 49 publications

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“…To distinguish a given nonlocal set, entanglement can be used as resource. There are several articles where entanglement in pure form was used to distinguish nonlocal sets [49,[53][54][55][56][57][58][59][60][61][62][63]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Distinguishability classes, resource sharing, and bound entanglement distribution

Halder

Sengupta

2020

Phys. Rev. A

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Suppose a set of m-partite, m ≥ 3, pure orthogonal fully separable states is given. We consider the task of distinguishing these states perfectly by local operations and classical communication (LOCC) in different k-partitions, 1 < k < m. Based on this task, it is possible to classify the sets of product states into different classes. For tripartite systems, a classification of the sets with explicit examples is presented. Few important cases related to the aforesaid task are also studied when the number of parties, m ≥ 4. These cases never appear for a tripartite system. However, to distinguish any LOCC indistinguishable set, entanglement can be used as resource. An important objective of the present study is to learn about the efficient ways of resource sharing among the parties. We also find an interesting application of multipartite product states which are LOCC indistinguishable in a particular k-partition. Starting from such product states, we constitute a protocol to distribute bound entanglement between two spatially separated parties by sending a separable qubit.

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Section: Introductionmentioning

confidence: 99%

Distinguishability classes, resource sharing, and bound entanglement distribution

Halder

Sengupta

2020

Phys. Rev. A

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“…Another direction of research is to explore entanglement as a resource to distinguish quantum states of nonlocal sets [49][50][51][52][53][54][55][56][57][58] by LOCC. In particular, the problem of distinguishing product states of given nonlocal sets by LOCC using entanglement as a resource was considered in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…[50], Cohen constructed entanglementassisted local protocols (protocols implementable by LOCC) to distinguish the orthogonal product states of several unextendible product bases. Later [56], separate entanglement-assisted local protocols were constructed to distinguish the states of a class of nonlocal bipartite COPBs. Recently [58], the problem of product state discrimination by LOCC was considered, where multiple copies of a maximally entangled state in C 2 ⊗C 2 are used as resource.…”

Section: Introductionmentioning

confidence: 99%

Several nonlocal sets of multipartite pure orthogonal product states

Halder

2018

Phys. Rev. A

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It is known that there exist sets of pure orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are nonlocal sets which exhibit nonlocality without entanglement. These nonlocal sets can be completable or uncompletable. In this work both completable and uncompletable small nonlocal sets of multipartite orthogonal product states are constructed. Apart from nonlocality, these sets have other interesting properties. In particular, the completable sets lead to the construction of a class of complete orthogonal product bases with the property that if such a basis is given then no state can be eliminated from that basis by performing orthogonality-preserving measurements. On the other hand, an uncompletable set of the present kind contains several Shifts unextendible product bases (UPBs) that belong to qubit subspaces. Identifying these subspace UPBs, it is possible to obtain a class of high-dimensional multipartite bound entangled states. Finally, it is shown that a two-qubit maximally entangled Bell state shared between any two parties is sufficient as a resource to distinguish the states of any completable set (of the above kind) perfectly by LOCC. This constitutes an example where the amount of entanglement, sufficient to accomplish the aforesaid task, depends neither on the dimension of the individual subsystems nor on the number of parties.

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“…In 2016, Zhang et al have shown that a C 2 ⊗ C 2 maximally entangled states is sufficient to perfectly distinguish certain classes by LOCC in C m ⊗C n [30] and have raised the question for a multipartite system. We believe that any class of locally indistinguishable orthogonal product states can be perfectly distinguished by LOCC with enough entanglements as resources.…”

Section: Introductionmentioning

confidence: 99%

Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource

Hai-quan

Jing

Tang

2018

Quantum Inf Process

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Recently, the method that using an entanglement as a resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has brought into focus. Zhang et al. presented protocols which use an entanglement to distinguish some classes of orthogonal product states in C m ⊗ C n [30]. In this paper, we mainly study the local distinguishability of multipartite product states. For the class of locally indistinguishable multipartite product states constructed by Wang et al. in [19], we present a protocol that distinguishes perfectly these quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.

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Entanglement as a resource to distinguish orthogonal product states

Cited by 37 publications

References 49 publications

Distinguishability classes, resource sharing, and bound entanglement distribution

Distinguishability classes, resource sharing, and bound entanglement distribution

Several nonlocal sets of multipartite pure orthogonal product states

Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource

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