Process POVM: A mathematical framework for the description of process tomography experiments

Abstract

In this paper we shall introduce the mathematical framework for the description of measurements of quantum processes. Using this framework the process estimation problems can be treated in the similar way as the state estimation problems, only replacing the concept of positive operator valued measure (POVM) by the concept of process POVM (PPOVM). In particular, we will show that any measurement of qudit channels can be described by a collection of effects (positive operators) defined on two-qudit system. However, the effects forming a PPOVM are not normalized in the usual sense. We will demonstrate the usage of this formalism in discrimination problems by showing that perfect channel discrimination is equivalent to a specific unambiguous state discrimination.