scholarly journals Nonexistence of entangled continuous-variable Werner states with positive partial transpose

2014 ◽  
Vol 89 (3) ◽  
Author(s):  
Daniel McNulty ◽  
Richard Tatham ◽  
Ladislav Mišta
Keyword(s):  
Continuous Variable ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Werner States

scholarly journals A family of norms with applications in quantum information theory

2011 ◽  
Vol 11 (1&2) ◽  
pp. 104-123
Author(s):  
Nathaniel Johnston ◽  
David W. Kribs
Keyword(s):  
Semidefinite Program ◽  
Constructive Proof ◽  
Convex Mapping ◽  
Semidefinite Programs ◽  
Positive Partial Transpose ◽  
The Family ◽  
Partial Transpose ◽  
Arbitrary Convex ◽  
Matlab Implementation ◽  
Werner States

We consider the problem of computing the family of operator norms recently introduced. We develop a family of semidefinite programs that can be used to exactly compute them in small dimensions and bound them in general. Some theoretical consequences follow from the duality theory of semidefinite programming, including a new constructive proof that for all r there are non-positive partial transpose Werner states that are r-undistillable. Several examples are considered via a MATLAB implementation of the semidefinite program, including the case of Werner states and randomly generated states via the Bures measure, and approximate distributions of the norms are provided. We extend these norms to arbitrary convex mapping cones and explore their implications with positive partial transpose states.

scholarly journals Entanglement distillation by extendible maps

2013 ◽  
Vol 13 (9&10) ◽  
pp. 751-770
Author(s):  
Lukasz Pankowski ◽  
Fernando G.S.L. Brandao ◽  
Michal Horodecki ◽  
Graeme Smith
Keyword(s):  
The State ◽  
Entangled States ◽  
Classical Communication ◽  
Positive Partial Transpose ◽  
Epr Pairs ◽  
Numerical Studies ◽  
Partial Transpose ◽  
Maximally Entangled States ◽  
Werner States ◽  
Open Question

It is known that from entangled states that have positive partial transpose it is not possible to distill maximally entangled states by local operations and classical communication (LOCC). A long-standing open question is whether maximally entangled states can be distilled from every state with a non-positive partial transpose. In this paper we study a possible approach to the question consisting of enlarging the class of operations allowed. Namely, instead of LOCC operations we consider $k$-extendible operations, defined as maps whose Choi-Jamio\l{}kowski state is $k$-extendible. We find that this class is unexpectedly powerful - e.g. it is capable of distilling EPR pairs even from completely product states. We also perform numerical studies of distillation of Werner states by those maps, which show that if we raise the extension index $k$ simultaneously with the number of copies of the state, then the class of $k$-extendible operations are not that powerful anymore and provide a better approximation to the set of LOCC operations.

scholarly journals Postponing Distillability Sudden Death in a Correlated Dephasing Channel

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 827
Author(s):  
Guanghao Xue ◽  
Liang Qiu
Keyword(s):  
Sudden Death ◽  
Quantum Channel ◽  
Positive Partial Transpose ◽  
Partial Correlations ◽  
Partial Transpose ◽  
Correlated Channel

We investigated the dynamics of a two-qutrit system in a correlated quantum channel. The partial correlations between consecutive actions of the channel can effectively postpone the phenomenon of distillability sudden death (DSD) and broaden the range of the time cutoff that indicates entanglement of the positive partial transpose states. Particularly, the negativity of the system will revive and DSD will disappear in the fully correlated channel.

scholarly journals Bound entanglement and distillability of multipartite quantum systems

2015 ◽  
Vol 13 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Hui Zhao ◽  
Xin-Yu Yu ◽  
Naihuan Jing
Keyword(s):  
Quantum Systems ◽  
Entangled States ◽  
Multipartite Quantum Systems ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Bound Entanglement

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.

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