FACIAL STRUCTURES FOR SEPARABLE STATES
FACIAL STRUCTURES FOR SEPARABLE STATES
The convex cone <TEX>$\mathbb{V}_1$</TEX> generated by separable states is contained in the cone <TEX>$\mathbb{T}$</TEX> of all positive semi-definite block matrices whose block transposes are also positive semi-definite. We characterize faces of the cone <TEX>$\mathbb{V}_1$</TEX> induced by faces of the cone <TEX>$\mathbb{T}$</TEX> which are determined by pairs of subspaces of matrices.