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

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

2011-06-07

arxiv.org/abs/1106.1247v1

Physics

Mathematical Physics

Scientific paper

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.

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