Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition

Agrawal, Sristy; Halder, Saronath; Banik, Manik

doi:10.1103/physreva.99.032335

Cited by 53 publications

(50 citation statements)

References 56 publications

(97 reference statements)

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“…Similar argument holds in case of other bipartitions and consequently B I I (3, 3) turns out to be a GNPB of Type-II. Note that this particular basis appears in a recent work for a different purpose [71].…”

Section: B Gnpb: Type-iimentioning

confidence: 91%

Genuinely nonlocal product bases: Classification and entanglement-assisted discrimination

et al. 2019

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An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication (LOCC) unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on state elimination property of the set via orthogonality-preserving measurements when all the parties are spatially separated or different subsets of the parties come together. We then study local state discrimination protocols for several such bases with additional entangled resources shared among the parties. Apart from consuming less entanglement than teleportation based schemes our protocols indicate operational significance of the proposed classification and exhibit nontrivial use of genuine entanglement in local state discrimination problem.

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Section: B Gnpb: Type-iimentioning

confidence: 91%

Genuinely nonlocal product bases: Classification and entanglement-assisted discrimination

et al. 2019

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“…We have that λ(S(x 0 = 0)) = |b| 2 = sin 2 (θ/2) and λ(S(x 0 = 1)) = |a| 2 = cos 2 (θ/2). For x 0 ∈ (0, 1) it is clear that we can restrict ourselves to the eigenvalues (24) for which the cosine is larger than zero. For a given such k we have (recall that |x 0 | 2 + |x 1 | 2 = 1):…”

Section: Acknowledgementsmentioning

confidence: 99%

Entanglement of genuinely entangled subspaces and states: Exact, approximate, and numerical results

Demianowicz

Augusiak

2019

Phys. Rev. A

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Genuinely entangled subspaces (GESs) are those subspaces of multipartite Hilbert spaces that consist only of genuinely multiparty entangled (GME) pure states. They are natural generalizations of the well-known notion of completely entangled subspaces (CESs), which by definition are void of fully product vectors. Entangled subspaces are an important tool of quantum information theory as they directly lead to construtions of entangled states, since any state supported on such a subspace is automatically entangled. Moreover, they have also proven useful in the area of quantum error correction (QEC). In our recent contribution [M. Demianowicz and R. Augusiak, Phys. Rev. A 98, 012313 (2018)], we have studied the notion of a GES qualitatively in relation to socalled nonorthogonal unextendible product bases and provided a few novel constructions of such subspaces. The main aim of the present work is to perform a quantitative study of the entanglement properties of GESs. First, we show how one can attempt to compute analytically the subspace entanglement, defined as the entanglement of the least entangled vector from the subspace, of a GES and illustrate our method applying it to a new class of GESs. Second, we show that certain semi-definite programming (SDP) relaxations can be exploited to estimate the entanglement of a GES and apply this observation to few classes of GESs revealing that in many cases the method provides the exact results. Finally, we study the entanglement of certain states supported on GESs, which is compared to the obtained values of the entanglement of the corresponing subspaces, and find the white noise robustness of several GESs. In our study we use the (generalized) geometric measure as the quantifier of entanglement.

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“…Primarily, these were completely entangled subspaces (CESs), that is, subspaces only with states that are in any way entangled [13][14][15]. Recently, we have witnessed an interest in so-called genuinely entangled subspaces (GESs), i.e., subspaces composed solely of genuinely multiparty entangled (GME) states, or, in other words, void of states displaying any form of separability [16][17][18][19]. The initial interest in CESs and GESs stemmed from the observation that (mixed) states supported on them are, respectively, entangled and GME.…”

Section: Introductionmentioning

confidence: 99%

An approach to constructing genuinely entangled subspaces of maximal dimension

Demianowicz¹,

Augusiak²

2020

Quantum Inf Process

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Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an application, for instance, in quantum error correction and cryptography. In a recent study (Demianowicz and Augusiak in Phys Rev A 98:012313, 2018), we have shown how GESs can be efficiently constructed in any multiparty scenario from the so-called unextendible product bases. The provided subspaces, however, are not of maximal allowable dimensions, and our aim here is to put forward an approach to building such. The method is illustrated with few examples in small systems. Connections with other mathematical problems, such as spaces of matrices of equal rank and the numerical range, are discussed. Keywords Genuinely entangled subspace • Genuinely multiparty entangled • Completely entangled subspace • Entanglement • Spaces of matrices of bounded rank Maciej Demianowicz

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Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition

Cited by 53 publications

References 56 publications

Genuinely nonlocal product bases: Classification and entanglement-assisted discrimination

Genuinely nonlocal product bases: Classification and entanglement-assisted discrimination

Entanglement of genuinely entangled subspaces and states: Exact, approximate, and numerical results

An approach to constructing genuinely entangled subspaces of maximal dimension

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