# 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)].

## 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

- MathematicsOpen 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…

Characterization and properties of weakly optimal entanglement witnesses

- Computer ScienceQuantum 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

- PhysicsQuantum 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.

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