Entanglement breaking channels

This paper studies the class of stochastic maps, or channels, for which (I circle times Phi)(Gamma) is always separable (even for entangled Gamma). Such maps are called entanglement breaking, and can always be written in the form Phi(rho) = Sigma(k) R-k Tr F(k)rho where each R-k is a density matrix and F-k > 0. If, in addition, Phi is trace-preserving, the {F-k} must form a positive operator valued measure (POVM). Some special classes of these maps are considered and other characterizations given. Since the set of entanglement-breaking trace-preserving maps is convex, it can be characterized by its extreme points. The only extreme points of the set of completely positive trace preserving maps which are also entanglement breaking are those known as classical-quantum or CQ. However, for d greater than or equal to 3, the set of entanglement breaking maps has additional extreme points which are not extreme CQ maps.