C∗-extreme points of entanglement breaking maps

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