On a characterization of positive maps

Abstract

Drawing on results of Choi, Stormer and Woronowicz, we present a nearly complete characterization of certain important classes of positive maps. In particular, we construct a general class of positive linear maps acting between two matrix algebras B(H) and B(K), where H and K are finite-dimensional Hilbert spaces. It turns out that elements of this class are characterized by operators from the dual cone of the set of all separable states on B(H ⊗ K). Subsequently, the relation between entanglements and positive maps is described. Finally, a new characterization of the cone B(H) + ⊗ B(K) + is given.