Facial structures for various notions of positivity
and applications to the theory of entanglement
by Seung-Hyeok Kye
arXiv:1202.4255
In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.