Exposed faces for decomposable positive linear maps arising from completely positive maps

Abstract

Let $D$ be a space of $2\times n$ matrices. Then the face of the cone of all completely positive maps from $M_2$ into $M_n$ given by $D$ is an exposed face of the bigger cone of all decomposable positive linear maps if and only if the set of all rank one matrices in $D$ forms a subspace of $D$ together with zero and $D^{\perp }$ is spanned by rank one matrices.

References in corpus (3)

• Generic local distinguishability and completely entangled subspaces
• Three-by-three bound entanglement with general unextendible product bases
• A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces