Exposed faces for decomposable positive linear maps arising from   completely positive maps
  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. 
Hyun-Suk Choi and Seung-Hyeok Kye
math-ph math.MP quant-ph