Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0110174 · Physical Review A

Characterization of distillable and activatable states using entanglement witnesses

Barbara Kraus, Maciej Lewenstein, J. I. Cirac

Published Apr 10, 2002• 40 citations
arXivHTMLPDF

Abstract

We introduce a formalism that connects entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in Eggeling et al. (e-print quant-ph/0104095), namely, that one copy of any bipartite state with nonpositive partial transpose (NPPT) is either distillable, or activatable. Second, we show that there exist three-partite NPPT states, with the property that two copies can neither be distilled, nor activated.

DOI
10.1103/physreva.65.042327

Related papers

Activating Distillation with an Infinitesimal Amount of Bound Entanglement

K. G. H. Vollbrecht, Michael M. Wolf

We show that bipartite quantum states of any dimension, which do not have a positive partial transpose (NPPT), become 1-distillable when one adds an infinitesimal amount of bound entanglement. To this end we investigate the activation properties of a new class of symmetric bound entangled states of full rank. It is shown that in this set there exist universal activator states capable of activating the distillation of any NPPT state. The result shows that even a small amount of bound entanglement can be useful for quantum information purposes.

arXiv:quant-ph/0201103•Physical Review Letters•May 31, 2002•51 citations

Correlated entanglement distillation and the structure of the set of undistillable states

Fernando G. S. L. Brandão, J. Eisert

We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: It is shown that for every entangled state σ and every k, there exists a copy-correlated k-undistillable state ρ such that σ⊗ρ is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a nonpositive partial transpose is discussed.

arXiv:0709.3835•Journal of Mathematical Physics•Apr 1, 2008•12 citations

A Few Steps More Towards NPT Bound Entanglement

Łukasz Pankowski, Marco Piani, Michał Horodecki +1 more

In this paper, existence of bound entangled states with nonpositive partial transpose (NPT) is considered. As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover, it would rule out a simple mathematical description of the set of distillable states. The particular state, known to be 1-copy nondistillable and supposed to be bound entangled, is considered. The problem of its two-copy distillability, which boils down to show that maximal overlap of some projectorQwith Schmidt rank two states does not exceed 1/2 (called thehalf-property), is studied. First, it is shown that the maximum overlap can be attained on vectors that are not of the simple product form with respect to cut between two copies. Then, the problem in attacked twofold way: (a) the half-property is proved for some wide classes of Schmidt rank two states; (b) the overlap forallSchmidt rank two states is bounded from above bycA⊗I+I⊗BwithA,Btraceless 4 × 4 matrices, and TrAfA+ TrBfB=1/4.

arXiv:0711.2613•IEEE Transactions on Information Theory•Jul 21, 2010•85 citations

Correlated entanglement distillation and the structure of the set of undistillable states

Fernando G. S. L. Brandão, Jens Eisert

We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically-distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: it is shown that for every entangled state σ and every k, there exists a copy-correlated k-undistillable state ρ such that σ ⊗ ρ is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a non-positive partial transpose is discussed. 1

•May 9, 2008•12 citations

Bound entanglement and distillability of multipartite quantum systems

Hui Zhao, Xin-Yu Yu, Naihuan Jing

We construct a class of entangled states in ℋ = ℋA ⊗ ℋB ⊗ ℋC quantum systems with dim ℋA = dim ℋB = dim ℋC = 2 and classify those states with respect to their distillability properties. The states are bound entanglement for the bipartite split (AB) - C. The states are non-positive partial transpose (NPT) entanglement and 1-copy undistillable for the bipartite splits A - (BC) and B - (AC). Moreover, we generalize the results of 2 ⊗ 2 ⊗ 2 systems to the case of 2n ⊗ 2n ⊗ 2n systems.

arXiv:1509.07425•International Journal of Quantum Information•Aug 1, 2015•1 citation

Distillability and partial transposition in bipartite systems

Wolfgang Dür, J. I. Cirac, Maciej Lewenstein +1 more

We study the distillability of a certain class of bipartite density operators which can be obtained via depolarization starting from an arbitrary one. Our results suggest that nonpositivity of the partial transpose of a density operator is not a sufficient condition for distillability, when the dimension of both subsystems is higher than 2.

arXiv:quant-ph/9910022•Physical Review A•May 17, 2000•221 citations
We introduce a formalism that connects entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in Eggeling et al. (e-print quant-ph/0104095), namely, that one copy of any bipartite state with nonpositive partial transpose (NPPT) is either distillable, or activatable. Second, we show that there exist three-partite NPPT states, with the property that two copies can neither be distilled, nor activated.
We show that bipartite quantum states of any dimension, which do not have a positive partial transpose (NPPT), become 1-distillable when one adds an infinitesimal amount of bound entanglement. To this end we investigate the activation properties of a new class of symmetric bound entangled states of full rank. It is shown that in this set there exist universal activator states capable of activating the distillation of any NPPT state. The result shows that even a small amount of bound entanglement can be useful for quantum information purposes.
We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: It is shown that for every entangled state σ and every k, there exists a copy-correlated k-undistillable state ρ such that σ⊗ρ is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a nonpositive partial transpose is discussed.
In this paper, existence of bound entangled states with nonpositive partial transpose (NPT) is considered. As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover, it would rule out a simple mathematical description of the set of distillable states. The particular state, known to be 1-copy nondistillable and supposed to be bound entangled, is considered. The problem of its two-copy distillability, which boils down to show that maximal overlap of some projectorQwith Schmidt rank two states does not exceed 1/2 (called thehalf-property), is studied. First, it is shown that the maximum overlap can be attained on vectors that are not of the simple product form with respect to cut between two copies. Then, the problem in attacked twofold way: (a) the half-property is proved for some wide classes of Schmidt rank two states; (b) the overlap forallSchmidt rank two states is bounded from above bycA⊗I+I⊗BwithA,Btraceless 4 × 4 matrices, and TrAfA+ TrBfB=1/4.
We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other. We hence replace the usually considered independent and identically-distributed hypothesis by the weaker assumption of merely having identical reductions. We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state. This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter. As an example of the usefulness of our approach to the study of entanglement distillation, we prove a new activation result, which generalizes earlier findings: it is shown that for every entangled state σ and every k, there exists a copy-correlated k-undistillable state ρ such that σ ⊗ ρ is single-copy distillable. Finally, the relation of our results to the conjecture about the existence of bound entangled states with a non-positive partial transpose is discussed. 1
We construct a class of entangled states in ℋ = ℋA ⊗ ℋB ⊗ ℋC quantum systems with dim ℋA = dim ℋB = dim ℋC = 2 and classify those states with respect to their distillability properties. The states are bound entanglement for the bipartite split (AB) - C. The states are non-positive partial transpose (NPT) entanglement and 1-copy undistillable for the bipartite splits A - (BC) and B - (AC). Moreover, we generalize the results of 2 ⊗ 2 ⊗ 2 systems to the case of 2n ⊗ 2n ⊗ 2n systems.