Operational extreme points of unital completely positive maps

TL;DR

This paper introduces new concepts of operational convex combinations and operational extreme points for unital completely positive maps, analyzing their properties and relationships within the set of such maps on matrix algebras.

Contribution

It defines operational convex combinations and operational extreme points, and characterizes their properties within the set of unital completely positive maps.

Findings

The set of ucp maps is the set of operational convex combinations of the identity.

Every automorphism is an operational extreme point.

Operational extreme points are not necessarily extreme points.

Abstract

Two notions for linear maps (operational convex combinations and operational exetreme points) are introduced. The set S of ucp maps on the n times n matrix algebra is the operational convex combinations of the identity map. An operational extreme point of S is an extreme point of S but the converse does not hold, and every automorphism is an operational extreme point of S.