# Optimal indecomposable witnesses without extremality as well as spanning property

@article{Ha2012OptimalIW,
title={Optimal indecomposable witnesses without extremality as well as spanning property},
author={Kil-Chan Ha and Hoseog Yu},
journal={arXiv: Quantum Physics},
year={2012}
}
• Published 4 June 2012
• Mathematics
• arXiv: Quantum Physics
One of the interesting problems on optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable witness which neither has the spanning property nor is associated with extremal positive linear map. Here, we answer this question negatively by examining the extremality of the positive linear maps constructed by Qi and Hou [J. Phys. A {\bf 44}, 215305 (2100)].
7 Citations
Indecomposability of entanglement witnesses constructed from any permutations
• Mathematics
• 2014
We present a way to construct indecomposable entanglement witnesses from any permutations π with π2 ≠ id for any finite dimensional bipartite systems. Some new bounded entangled states are also
Exposedness of Choi-Type Entanglement Witnesses and Applications to Lengths of Separable States
• Mathematics
Open Syst. Inf. Dyn.
• 2013
A large class of indecomposable exposed positive linear maps between 3 × 3 matrix algebras and two-qutrit separable states with lengths ten are presented.
Optimality of entanglement witnesses constructed from arbitrary permutations
• Mathematics, Computer Science
Quantum Inf. Process.
• 2015
A class of optimal entanglement witnesses constructed by permutations is obtained.
The structural physical approximation conjecture
It was conjectured that the structural physical approximation (SPA) of an optimal entanglement witness is separable (or equivalently, that the SPA of an optimal positive map is entanglement
Characterization and properties of weakly optimal entanglement witnesses
• Computer Science
Quantum Inf. Comput.
• 2015
We present an analysis of the properties and characteristics of weakly optimal entanglement witnesses, that is witnesses whose expectation value vanishes on at least one product vector. Any weakly
Indecomposability of entanglement witnesses
• Physics
Quantum Inf. Comput.
• 2015
There is no universal EW W so that every entangled state can be detected by W, so constructing as many as possible EWs is important to detect entanglement in states.

## References

SHOWING 1-10 OF 43 REFERENCES
One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps
• Mathematics
• 2011
In a recent paper [D. Chru\ifmmode \acute{s}\else \'{s}\fi{}ci\ifmmode \acute{n}\else \'{n}\fi{}ski and F. A. Wudarski, Open Sys. Information Dyn. (unpublished)], it was conjectured that the
Characterization of optimal entanglement witnesses
• Mathematics
• 2012
In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying
Entanglement Witnesses Arising from Exposed Positive Linear Maps
• Mathematics
Open Syst. Inf. Dyn.
• 2011
We consider entanglement witnesses arising from positive linear maps which generate exposed extremal rays. We show that every entangled state can be detected by one of these witnesses, and this
Geometry of Entanglement Witnesses for Two Qutrits
• Mathematics
Open Syst. Inf. Dyn.
• 2011
It is conjecture that maps parameterized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement.
Optimal decomposable witnesses without the spanning property
• Mathematics
• 2011
One of the unsolved problems in the characterization of the optimal entanglement witnesses is the existence of optimal witnesses acting on bipartite Hilbert spaces
Extremal extensions of entanglement witnesses: Finding new bound entangled states
• Computer Science
• 2011
The constructions are based on a generalization of the Choi map, from which the extremal extensions of entanglement witnesses are constructed, and the Cholesky-like decomposition is used to construct entangled states which are revealed by these extremal entangler witnesses.
Positive maps, positive polynomials and entanglement witnesses
• Mathematics
• 2009
We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block
Optimization of entanglement witnesses
• Physics
• 2000
An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an
Characterization of separable states and entanglement witnesses
• Mathematics
• 2001
We provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for
Spectral properties of entanglement witnesses
Entanglement witnesses are observables which when measured, detect entanglement in a measured composed system. It is shown what kind of relations between eigenvectors of an observable should be