Facial Structures for Positive Linear Maps in the Two Dimensional Matrix Algebra
by Eung-Soo Byeon and Seung-Hyeok Kye
Positivity, 6 (2002), 369-380

We completely determine the lattice structure for the faces of the convex cone of all positive linear maps between the $2\times 2$ matrix algebras, in terms of pairs of subspaces of $M_2$.