Optimal bounded-error strategies for projective measurements in non-orthogonal state discrimination

TL;DR

This paper investigates optimal projective measurement strategies that minimize inconclusive results within a bounded-error rate in non-orthogonal quantum state discrimination, bridging the gap between unambiguous and minimum error approaches.

Contribution

It introduces a theoretical framework for optimal projective measurements in bounded-error discrimination, expanding beyond traditional POVM strategies.

Findings

Derived constraints for generalized measurements (POVMs)

Identified optimal projective measurement strategies within the bounded-error range

Compared projective strategies to POVMs and experimental UD implementations

Abstract

Research in non-orthogonal state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error (ME) discrimination. This paper explores the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements (POVMs). We then provide the theory for the optimal projective measurement (PVM) in this range. Through analytical and numerical results we investigate this family of projective, bounded-error strategies and compare it to the POVM family as well as to experimental implementation of UD using POVMs. We also discuss a possible application of these bounded-error strategies to quantum key distribution.