Nonlocality of orthogonal product-basis quantum states

Wang, Yanling; Li, Maosheng; Zheng, Zhu-Jun; Fei, Shao-Ming

doi:10.1103/physreva.92.032313

Cited by 97 publications

(56 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the states of our construction are less than the states in [26] and are not unextendible product bases [12], either. For example, the following product state |φ 3n+m−3 = |0 A |0 B is orthogonal to the states in (1).…”

Section: Local Indistinguishability Of Orthogonal Product Statesmentioning

confidence: 94%

See 1 more Smart Citation

Local indistinguishability of orthogonal product states

et al. 2016

View full text Add to dashboard Cite

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.

show abstract

Section: Local Indistinguishability Of Orthogonal Product Statesmentioning

confidence: 94%

“…And most of these states are extendible. In addition, the two classes of orthogonal product states of our construction are less than the states in [26].…”

Section: Introductionmentioning

confidence: 96%

Local indistinguishability of orthogonal product states

et al. 2016

View full text Add to dashboard Cite

show abstract

“…A similar construction of completable set of locally indistinguishable states also follows from the Refs. [59,60]. However, the cardinality there will be higher than 14.…”

Section: State Discrimination By Loccmentioning

confidence: 96%

Family of bound entangled states on the boundary of the Peres set

2019

View full text Add to dashboard Cite

Bound entangled (BE) states are strange in nature: non-zero amount of free entanglement is required to create them but no free entanglement can be distilled from them under local operations and classical communication (LOCC). Even though usefulness of such states has been shown in several information processing tasks, there exists no simple method to characterize them for an arbitrary composite quantum system. Here we present a (d − 3)/2-parameter family of BE states each with positive partial transpose (PPT). This family of PPT-BE states is introduced by constructing an unextendible product basis (UPB) in C d ⊗ C d with d odd and d ≥ 5. The range of each such PPT-BE state is contained in a 2(d − 1) dimensional entangled subspace whereas the associated UPB-subspace is of dimension (d − 1) 2 + 1. We further show that each of these PPT-BE states can be written as a convex combination of (d − 1)/2 number of rank-4 PPT-BE states. Moreover, we prove that these rank-4 PPT-BE states are extreme points of the convex compact set P of all PPT states in C d ⊗ C d , namely the Peres set. An interesting geometric implication of our result is that the convex hull of these rank-4 PPT-BE extreme points -the (d − 3)/2-simplex -is sitting on the boundary between the set P and the set of non-PPT states. We also discuss consequences of our construction in the context of quantum state discrimination by LOCC.

show abstract

“…For the outcome 11,12,13,14) invariant. Then, Charles can identify these states by four projectors C 9i = |i C i|, i = 1, 2, 3, 4.…”

Section: Local Distinguishability For Odd-partite Casementioning

confidence: 99%

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

Hai-quan

Jing

Tang

2018

Quantum Inf Process

View full text Add to dashboard Cite

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.

show abstract

Nonlocality of orthogonal product-basis quantum states

Cited by 97 publications

References 36 publications

Local indistinguishability of orthogonal product states

Local indistinguishability of orthogonal product states

Family of bound entangled states on the boundary of the Peres set

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

Contact Info

Product

Resources

About