An analysis of completely-positive trace-preserving maps on image Original Research Article

We give a useful new characterization of the set of all completely positive, trace-preserving maps image from which one can easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non-unital extreme points that can be characterized as having exactly two images on the Bloch sphere. We also discuss a number of related issues about the images and the geometry of the set of stochastic maps, and show that any stochastic map on image can be written as a convex combination of two “generalized” extreme points.