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

Halder, Saronath; Banik, Manik; Ghosh, Sibasish

doi:10.1103/physreva.99.062329

Cited by 35 publications

(29 citation statements)

References 62 publications

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“…Given the difficulties in detecting and quantifying entangled states in general and more so for multipartite genuine entanglement, construction of subspaces possessing such properties apriori is a systematic way forward. Several algorithms for constructing completely entangled subspaces (CES) -subspace containing no product vector -are known for bipartite as well as multipartite scenarios [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. However, in a multipartite scenario, as entanglement appears in different inequivalent forms, a coherent formalism to construct subspaces containing only a particular type of entanglement is more demanding.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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In a multipartite scenario quantum entanglement manifests its most dramatic form when the state is genuinely entangled. Such a state is more beneficial for information theoretic applications if it contains distillable entanglement in every bipartition. It is, therefore, of significant operational interest to identify subspaces of multipartite quantum systems that contain such properties apriori. In this letter, we introduce the notion of unextendible biseparable bases (UBB) that provides an adequate method to construct genuinely entangled subspaces (GES). We provide explicit construction of two types of UBBs -party symmetric and party asymmetric -for every 3-qudit quantum system, with local dimension d ≥ 3. Further we show that the GES resulting from the symmetric construction is indeed a bidistillable subspace, i.e., all the states supported on it contain distillable entanglement across every bipartition.

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Section: Introductionmentioning

confidence: 99%

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

2019

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“…We are now ready to give a systematic protocol to do so: (i) Consider the class of UPBs for which if the stopper is removed from the UPB then the rest is extendible to a full basis, e.g., UPBs which are given in Refs. [13,15,30]. (ii) Following these constructions, it is possible to construct real UPBs of the above kind.…”

Section: Resultsmentioning

confidence: 99%

Construction of noisy bound entangled states and the range criterion

Halder

Sengupta

2019

Physics Letters A

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In this work we consider bipartite noisy bound entangled states with positive partial transpose, that is, such a state can be written as a convex combination of an edge state and a separable state. In particular, we present schemes to construct distinct classes of noisy bound entangled states which satisfy the range criterion. As a consequence of the present study we also identify noisy bound entangled states which do not satisfy the range criterion. All of the present states are constituted by exploring different types of product bases.One of the key developments within the theory of quantum entanglement [1,2], is the invention of bound entangled states [3]. These states are mixed entangled states from which entanglement in pure form cannot be extracted by local operations and classical communication [4]. This holds true even if large number of identical copies of the state are shared among spatially separated parties. Since the discovery of bound entangled states, there is no simple technique to identify such states. Therefore, it is highly nontrivial to present new classes of bound entangled states. For a given bipartite quantum state if the state produces negative eigenvalue(s) under partial transpose then it guarantees inseparability of that state [5]. The problem arises when the given state remains positive under partial transpose (PPT). In such a situation it is not always easy to conclude whether the state is separable or inseparable (entangled). Generally, for an arbitrary bipartite PPT state if the dimension of the corresponding Hilbert space is greater than 6 then it is difficult to say whether the state is separable or inseparable [6]. In fact, the problem of determining any density matrix -separable or entangled is a NP-hard problem [7]. However, if a PPT state is entangled then the state must be bound entangled [4]. On the other hand existence of bound entangled states with negative partial transpose is conjectured and remains open till date [8][9][10].Application of the range criterion is quite effective approach to prove the inseparability a given PPT state [3]. For a given bipartite density matrix ρ, if the state is separable then there exists a set of product states {|θ i 1 ⊗ |θ i 2 } that spans the range of ρ while the set of product states {|θ i 1 ⊗ |θ * i 2 } spans the range of ρ t . Here, the superscript t denotes the partial transpose operation (considering second subsystem) and * denotes the complex conjugation in a basis with respect to which the partial transpose is taken. Any state which violates the range criterion is an entangled state. However, there exist several classes of PPT entangled states which satisfy the range criterion [11,12]. Evidently, detection of such states are one of the troublesome tasks in the entanglement theory. Therefore, to understand these states in a better way, it is important to constitute such states. Note that a full-rank state trivially satisfy the range criterion. So, it is significant to understand the forms of distinct classes of low-rank bound entang...

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“…In this section, we will present two different entanglement assisted discrimination protocols. First, we show a class of UPB in 5 ⊗ 5 as follows, which has the structure of Fig.1 [36]. The state |F , known as the stopper state, is not shown, as it would cover the whole diagram.…”

Section: Entanglement Assisted Discriminationmentioning

confidence: 99%

“…For the above UPB, the authors of [36] have presented that their nontrivial construction attributes a notable property compared to the trivial one which is always possible to distinguish few states perfectly from the UPB by orthogonality preserving LOCC. But in their case, not even a single state can be perfectly distinguished by such LOCC.…”

Section: Entanglement Assisted Discriminationmentioning

confidence: 99%

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Locally distinguishing unextendible product bases by using entanglement efficiently

Zhang

2020

Phys. Rev. A

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Any set of states which cannot be perfectly distinguished by local operations and classical communication (LOCC) alone, can always be locally distinguished using quantum teleportation with enough entanglement resource. However, in quantum information theory, entanglement is a very valuable resource, so it leaves the following open question: how to accomplish this task more efficiently than teleportation, that is, design the local discrimination protocol using less entanglement resource. In this paper, we first present two protocols to locally distinguish a set of unextendible product bases (UPB) in 5 ⊗ 5 by using different entanglement resource. Then, we generalize the distinguishing methods for a class of UPB in d ⊗ d, where d is odd and d 3. Furthermore, for a class of UPB in d ⊗ d, where d is even and d 4, we prove that these states can also be distinguished by LOCC with multiple copies of low-dimensional entanglement resource. These results offer rather general insight into how to use entanglement resource more efficiently, and also reveal the phenomenon of less nonlocality with more entanglement.

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

Cited by 35 publications

References 62 publications

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

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

Construction of noisy bound entangled states and the range criterion

Locally distinguishing unextendible product bases by using entanglement efficiently

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