# Distillability via protocols respecting the positivity of partial transpose.

@article{Eggeling2001DistillabilityVP,
title={Distillability via protocols respecting the positivity of partial transpose.},
author={T. Eggeling and K. Vollbrecht and R. Werner and M. Wolf},
journal={Physical review letters},
year={2001},
volume={87 25},
pages={
257902
}
}
• T. Eggeling, +1 author M. Wolf
• Published 2001
• Mathematics, Medicine, Physics
• Physical review letters
We show that all quantum states that do not have a positive partial transpose are distillable via channels, which preserve the positivity of the partial transpose. The question whether bound entangled states with non-positive partial transpose exist is therefore closely related to the connection between the set of separable superoperators and positive partial transpose-preserving maps.
39 Citations

#### Topics from this paper

Entanglement distillation by extendible maps
• Computer Science, Physics
• Quantum Inf. Comput.
• 2013
This paper studies a possible approach to the question of whether maximally entangled states can be distilled from every state with a non-positive partial transpose by enlarging the class of operations allowed, and considers k-extendible operations, defined as maps whose Choi-Jamio lkowski state is k-Extendible. Expand
Bound entanglement and distillability of multipartite quantum systems
• Physics
• 2015
We construct a class of entangled states in ℋ = ℋA ⊗ ℋB ⊗ ℋC quantum systems with dimℋA = dimℋB = dimℋC = 2 and classify those states with respect to their distillability properties. The states areExpand
A Few Steps More Towards NPT Bound Entanglement
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2010
The particular state, known to be 1-copy nondistillable and supposed to be bound entangled, is considered, and the problem of its two-copy distillability, which boils down to show that maximal overlap of some projector with Schmidt rank two states does not exceed 1/2 is studied. Expand
Entanglement manipulation and distillability beyond LOCC
• Physics
• 2017
When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communicationExpand
NONDISTILLABLE ENTANGLEMENT GUARANTEES DISTILLABLE ENTANGLEMENT
• Mathematics, Physics
• 2011
The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with theExpand
Entanglement manipulation beyond local operations and classical communication
• E. Chitambar, Julio I. de Vicente
• Physics, Computer Science
• 2020
This paper demonstrates that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and shows that any two states can be interconverted by any polytope approximation to the set of separable channels. Expand
One-shot entanglement distillation beyond local operations and classical communication.
• Physics, Computer Science
• 2019
The $\varepsilon$-error one-shot distillable entanglement of any pure state is the same under all sets of operations ranging from one-way LOCC to separability-preserving operations or operations preserving the set of states with positive partial transpose, and can be computed exactly as a quadratically constrained linear program. Expand
One-Shot Rates for Entanglement Manipulation Under Non-entangling Maps
• Mathematics, Physics
• IEEE Transactions on Information Theory
• 2011
By considering the limit of many identical copies of the shared entangled state, this work partially recover the recently found reversibility of entanglement manipulation under the class of operations which asymptotically do not generateEntanglement. Expand
Entangling capacities and the geometry of quantum operations
• Medicine, Physics
• Scientific reports
• 2020
The bounds of entangling capacity are found to be associated with how non-PPT (PPT preserving) an operation is, and the equivalence of PPT-ness and separability for unitary operations is demonstrated. Expand
Entanglement distillation : a discourse on bound entanglement in quantum information theory
This thesis covers in a unified way the material presented in quant-ph/0403073,quantity/0502040, quant-Ph/0504160, quants/0510035, quant/0512012 and quant- ph/0603283. Expand

#### References

SHOWING 1-7 OF 7 REFERENCES
Phys
• Rev. Lett. 86, 2681
• 2001
Phys
• Rev. Lett. 80, 5239
• 1998
Phys
• Rev. A 61, 062312
• 2000
Phys
• Rev. A 61, 062313
• 2000
Phys
• Rev. A 59, 4206 (1999); S.L. Braunstein, C.M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. 83, 1054
• 1999
Phys
• Rev. Lett. 74, 2619
• 1995
Phys
• Rev. A, 40, 4277
• 1989