Operating Characteristics for Classical and Quantum Binary Hypothesis Testing

Abstract

This monograph addresses operating characteristics for binary hypothesis testing in both classical and quantum settings and overcomplete quantum measurements for quantum binary state discrimination. We specifically explore decision and measurement operating characteristics defined as the tradeoff between probability of detection and probability of false alarm as parameters of the pre-decision operator and the binary decision rule are varied. In the classical case we consider in detail the Neyman-Pearson optimality of the operating characteristics when they are generated using threshold tests on a scalar score variable rather than threshold tests on the likelihood ratio. In the quantum setting, informationally overcomplete POVMs are explored to provide robust quantum binary state discrimination. We focus on equal trace rank one POVMs which can be specified by arrangements of points on a sphere that we refer to as an Etro sphere. Catherine A. Medlock and Alan V. Oppenheim (2021), “Operating Characteristics for Classical and Quantum Binary Hypothesis Testing”, Foundations and Trends® in Signal Processing: Vol. 15, No. 1, pp 1–120. DOI: 10.1561/2000000106. Full text available at: http://dx.doi.org/10.1561/2000000106