Optimal indecomposable witnesses without extremality as well as spanning property

Abstract

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)].

17 pages

References in corpus (4)

• Necessary and sufficient conditions for bipartite entanglement
• Entanglement witnesses arising from exposed positive linear maps
• Spectral properties of entanglement witnesses
• A characterization of optimal entanglement witnesses

Cited by in corpus (4)

• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states
• Extremal extensions of entanglement witnesses and their connection with UPB
• Internal Boundary between Entanglement and Separability Within a Quantum State
• A class of generalized positive linear maps on matrix algebras