Subspace preserving completely positive maps

A class of quantum channels and completely positive maps (CPMs) are introduced and investigated. These, which we call subspace preserving (SP) CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve probability weights on a given orthogonal sum decomposition of the Hilbert space of a quantum system. Several equivalent characterizations of SP CPMs are proved and an explicit construction of all SP CPMs, is provided. For a subclass of the SP channels a construction in terms of joint unitary evolution with an ancilla system, is presented.