Discrimination of quantum observables using limited resources

TL;DR

This paper investigates how to distinguish quantum observables unambiguously with limited resources, especially focusing on qubit observables, and establishes conditions for perfect and inconclusive discrimination.

Contribution

It provides a general framework for discriminating quantum observables and characterizes the conditions under which perfect or inconclusive discrimination is possible for qubit observables.

Findings

Perfect discrimination with two shots is only possible for sharp, mutually orthogonal qubit observables.

Unambiguous discrimination with inconclusive results is always possible for sharp qubit observables with nonorthogonal directions.

The study advances understanding of resource-limited quantum measurement discrimination.

Abstract

We address the problem of unambiguous discrimination and identification among quantum observables. We set a general framework and investigate in details the case of qubit observables. In particular, we show that perfect discrimination with two shots is possible only for sharp qubit observables (e.g. Stern-Gerlach apparatuses) associated with mutually orthogonal directions. We also show that for sharp qubit observables associated to nonorthogonal directions unambiguous discrimination with an inconclusive result is always possible.