BURES DISTANCE FOR alpha-COMPLETELY POSITIVE MAPS AND TRANSITION PROBABILITY BETWEEN P-FUNCTIONALS

Abstract

In this paper we discuss the Bures distance between alpha-CP maps on a C*-algebra and the transition probability between P-functionals on a *-algebra. We first review the notion of alpha-CP maps and the representation theorem associated to alpha-CP maps. Using the Krein space representation and the set of intertwiners between Krein space representations, we study the Bures distance between alpha-CP maps. We prove that the transition probability between P-functionals can be estimated by some functionals using J-representations on Krein spaces.