This paper studies the class of stochastic maps, or channels, whose action
(when tensored with the identity) on an entangled state always yields a
separable state. Such maps have a canonical form introduced by Holevo. Such
maps are called entanglement breaking, and can always be written in a canonical
form introduced by Holevo. Some special classes of these maps are considered
and several equivalent characterizations given.
Since the set of entanglement-breaking trace-preserving maps is convex, it
can be described 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 > 2 the set of
entanglement breaking maps has additional extreme points which are not extreme
CQ maps.