# 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} }

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)].

## 8 Citations

Indecomposability of entanglement witnesses constructed from any permutations

- Mathematics, Physics
- 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, PhysicsOpen 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 ScienceQuantum Inf. Process.
- 2015

A class of optimal entanglement witnesses constructed by permutations is obtained.

The structural physical approximation conjecture

- Mathematics
- 2016

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…

Entanglement witnesses: construction, analysis and classification

- Computer Science, Mathematics
- 2014

The theory of EWs finds elegant geometric formulation in terms of convex cones and related geometric structures and this work focuses on theoretical analysis of various important notions like decomposability, atomicity, optimality, extremality and exposedness.

Characterization and properties of weakly optimal entanglement witnesses

- Computer Science, MathematicsQuantum 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…

A class of generalized positive linear maps on matrix algebras

- Mathematics
- 2013

Abstract We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic…

Indecomposability of entanglement witnesses

- Computer ScienceQuantum 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

- Physics, 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

- Physics, 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, PhysicsOpen 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, PhysicsOpen 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

- Physics
- 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

- Physics
- 2011

In this paper, we discuss extremal extensions of entanglement witnesses based on Choi's map. The constructions are based on a generalization of the Choi map, from which we construct entanglement…

Positive maps, positive polynomials and entanglement witnesses

- Mathematics, Physics
- 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

- Physics
- 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

- Mathematics, Physics
- 2008

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…