C∗-extreme points of entanglement breaking maps

In this paper, we study the C∗-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of C∗-extreme points are discussed. By establishing a Radon-Nikodym-type theorem for a class of EB-maps we give a complete description of the C∗-extreme points. It is shown that a unital EB-map: Md1 -Md2 is C∗-extreme if and only if it has Choi-rank equal to d2. Finally, as a direct consequence of the Holevo form of EB-maps, we derive a non-commutative analog of the Krein-Milman theorem for C∗-convexity of the set of unital EB-maps.