Receiver operation characteristics of quantum state discrimination

TL;DR

This paper applies receiver operation characteristics analysis to quantum state discrimination, introducing a quantum Bhattacharyya coefficient to quantify state similarity and providing a new perspective on quantum measurement performance.

Contribution

It introduces a quantum generalization of the classical Bhattacharyya coefficient and applies ROC analysis to quantum state discrimination, offering new tools for quantum state comparison.

Findings

ROC diagrams effectively represent quantum state discrimination.

Quantum Bhattacharyya coefficient quantifies quantum state similarity.

Properties of the quantum Bhattacharyya coefficient suggest its usefulness in quantum information.

Abstract

We provide a description of the problem of the discrimination of two quantum states in terms of receiver operation characteristics analysis, a prevalent approach in classical statistics. Receiveroperation characteristics diagrams provide an expressive representation of the problem, in which quantities such as the fidelity and the trace distance also appear explicitly. In addition we introduce an alternative quantum generalization of the classical Bhattacharyya coefficient. We evaluate our quantum Bhattacharyya coefficient for certain situations and describe some of its properties. These properties make it applicable as another possible quantifier of the similarity of quantum states.