Extremal matrix states on tensor product of \(C^{*}\)-algebras (Q398695)

A matrix state on a unital \(C^\ast\)-algebra \(A\) is a unital, completely positive, linear map \(A\to \mathbb M_n\) where \(n\in\mathbb N\). The matrix state space \(\mathcal{CS}(A)\) is the set of all matrix states on \(A\). It can be expressed as \(\bigcup_{n}K_n\) where \(K_n\subseteq M_n(A^\ast)\) and it is matrix convex. The present paper describes the matrix extremal points of \(\mathcal{CS}(A)\) when \(A\) is the tensor product of two unital \(C^\ast\)-algebras and at least one of them is of type I.