Disturbance by optimal discrimination

TL;DR

This paper investigates the effects of optimal quantum measurements designed for unambiguous state discrimination, proving that such measurements inevitably alter states in a way that makes previously distinguishable states indistinguishable when outcomes are inconclusive.

Contribution

The authors remove previous restrictions on measurement classes and state count, providing general theorems applicable to infinite candidate states and broadening understanding of measurement disturbance.

Findings

Optimal measurements cause indistinguishability in inconclusive outcomes.

Theorems apply to infinitely many candidate states.

Mathematical conditions for post-measurement states are established.

Abstract

We discuss the disturbance by measurements which unambiguously discriminate between given candidate states. We prove that such an optimal measurement necessarily changes distinguishable states indistinguishable when the inconclusive outcome is obtained. The result was previously shown by Chefles~[Phys. Lett. A 239, 339 (1998)] under restrictions on the class of quantum measurements and on the definition of optimality. Our theorems remove these restrictions and are also applicable to infinitely many candidate states. Combining with our previous results, one can obtain concrete mathematical conditions for the resulting states. The method may have a wide variety of applications in contexts other than state discrimination.