Distillability via Protocols Respecting the Positivity of Partial Transpose

Eggeling, Tilo; Vollbrecht, K. G. H.; Werner, R. F.; Wolf, Michael M.

doi:10.1103/physrevlett.87.257902

Cited by 64 publications

(55 citation statements)

References 12 publications

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“…One may prove this in almost the same manner as [17,18] where trace-preserving PPT maps have been considered. S is a CP map if and only if…”

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confidence: 74%

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Bound Entanglement Provides Convertibility of Pure Entangled States

Ishizaka

2004

Phys. Rev. Lett.

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I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. Similar effect of bound entanglement occurs in three qubits where two incomparable entangled states of GHZ and W can be inter-converted. In general multipartite settings composed by N distant parties, all N -partite pure entangled states are interconvertible by SLOCC with the assistance of bound entangled states with positive partial transpose.PACS numbers: 03.67. Mn, 03.65.Ud In quantum entanglement processing, the transformation of entangled states by local operations and classical communication (LOCC) is a basic task, where many intriguing aspects concerning convertibility and irreversibility appear. All bipartite pure entangled states are inter-convertible in the asymptotic transformation [1] where infinitely many identical copies of states are processed. Therefore, all bipartite pure entangled states can be used to perform the same task of entanglement processing in the asymptotic regime. However, there exists a restriction in the transformation of a single copy of bipartite pure states ( Fig. 1): two distant parties cannot increase the number of superposed terms (Schmidt rank, the rank of the reduced density matrix) by LOCC even in a stochastic manner (such stochastic LOCC is denoted by SLOCC) [2,3,4]. As a result, bipartite entanglement is classified by the Schmidt rank from the viewpoint of the convertibility at the single copy level [5]. Such restriction becomes more strict in multipartite settings. In three qubits, there are two different types of tripartite entanglement: GHZ and W type [5] [the GHZ state is (|111 +|222 )/ √ 2 and W state is (|112 +|121 +|211 )/ √ 3]. These cannot be transformed to each other by SLOCC, and such entangled states are said to be incomparable (Fig. 2). In general multipartite settings composed by N distant parties, there are many (possibly infinitely many) incomparable types of N -partite entanglement.On the other hand, a remarkable aspect of the irreversibility is the existence of bound entangled (BE) states [6]. Distant parties need to consume pure entangled states to prepare BE states, but they cannot distill pure entangled states from it any more. Much attention has been paid to this weak type of entanglement to clarify its properties and usefulness for quantum information processing. BE states by itself are useless for both quantum teleportation [7] and superdense coding [8]. However, it has been shown that BE states can activate the bound entanglement of the other state [9] and are useful for secure key distribution [10] In this paper, I show that BE states strongly influence the entanglement processing of pure states at the single copy level. Two distant parties can get capability to increase the Schmidt rank of bipartite pure entangled s...

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“…One may prove this in almost the same manner as [17,18] where trace-preserving PPT maps have been considered. S is a CP map if and only if…”

mentioning

confidence: 74%

“…PPT states are undistillable, and hence entangled PPT states are BE states [6]. The effects of such PPT-BE states can be taken into account by considering the PPT maps which preserve the positivity of the partial transpose [16,17,18,19,20,21]. Among such PPT maps, stochastic PPT maps of non-trace-preserving are considered.…”

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confidence: 99%

Bound Entanglement Provides Convertibility of Pure Entangled States

Ishizaka

2004

Phys. Rev. Lett.

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“…There, entanglement manipulation was studied under the class of operations that maps every state with a positive partial transpose (PPT) into another PPT state (including the use of ancillas). It was realized in [33] that every state with a nonpositive partial transpose becomes distillable under PPT preserving operations. This eliminates the phenomenon of bound entanglement in a qualitative level thereby suggesting the possibility of reversibility in this setting.…”

Section: A Previous Work and Related Approachesmentioning

confidence: 99%

A Reversible Theory of Entanglement and its Relation to the Second Law

Brandão

Plenio

2010

Commun. Math. Phys.

171

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We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandão and Plenio, Nature Physics 4, 8 (2008)], and in stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement.Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein's Lemma proved in [Brandão and Plenio, Commun. Math. 295, 791 (2010)], giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.

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“…We apply this formalism to two cases: First, we rederive the results presented in [42], namely that one copy of any bipartite state with non-positive partial transpose is either distillable, or activable. Second, we show that there exist three-partite NPPT states, with the property that two copies can neither be distilled, nor activated.…”

Section: B Results On Witness Operatorsmentioning

confidence: 99%

Entanglement Properties of Composite Quantum Systems

Eckert

Gühne

Hulpke

et al. 2003

Quantum Information Processing

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We present here an overview of our work concerning entanglement properties of composite quantum systems. The characterization of entanglement, i.e. the possibility to assert if a given quantum state is entangled with others and how much entangled it is, remains one of the most fundamental open questions in quantum information theory. We discuss our recent results related to the problem of separability and distillability for distinguishable particles, employing the tool of witness operators. Finally, we also state our results concerning quantum correlations for indistinguishable particles.

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Distillability via Protocols Respecting the Positivity of Partial Transpose

Cited by 64 publications

References 12 publications

Bound Entanglement Provides Convertibility of Pure Entangled States

Bound Entanglement Provides Convertibility of Pure Entangled States

A Reversible Theory of Entanglement and its Relation to the Second Law

Entanglement Properties of Composite Quantum Systems

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