Entanglement witnesses arising from exposed positive linear maps
We consider entanglement witnesses arising from positive linear maps
which generate exposed extremal rays. We show that every
entanglement can be detected by one of these witnesses, and this
witness detects a unique set of entanglement among those.
Therefore, they provide a minimal set of witnesses
to detect all entanglement in a sense.
Furthermore, if those maps are indecomposable then they detect
large classes of entanglement with positive partial
transposes which have nonempty relative interiors in the cone
generated by all PPT states. We also provide a one parameter
family of indecomposable positive linear maps which generate
exposed extremal rays. This gives the first examples of such maps
between three dimensional matrix algebra.
by Kil-Chan Ha and Seung-Hyeok Kye
Open Syst. Inf. Dyn.
18 (2011), 323-337.