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Let PI (respectively CPI) be the convex compact set of all unital positive (respectively completely positive) linear maps from the matrix algebra Mm([Copf ]) into Mn([Copf ]). We show that maximal faces of CPI correspond to one dimensional subspaces of the vector space Mm, n([Copf ]). Furthermore, a maximal face of CPI lies on the boundary of PI if and only if the corresponding subspace is generated by a rank one matrix.
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