Receiver Operation Characteristics of Quantum State Discrimination

Abstract

We describe the ambiguous discrimination of two quantum states using the receiver operation characteristics (ROC) analysis, an approach prevalent in classical statistics. We obtain a new comprehensive picture of this otherwise well-studied problem, in which various important quantities such as the fidelity and the trace distance of two quantum states obtain an operational meaning in a very intuitive way. In addition, we introduce a new quantity which is a generalization of the classical Bhattacharyya coefficient to the quantum scenario different from the one prevalently used in the literature. This derives logically from the ROC representation and provides an alternative characterization of the similarity of two quantum states. We describe some its properties, including the monotony under completely positive maps.