Optimized maximum-confidence discrimination of N mixed quantum states and application to symmetric states

TL;DR

This paper develops an optimized measurement strategy for discriminating N mixed quantum states with maximum confidence and minimal inconclusive outcomes, including analytical solutions for symmetric states and specific examples.

Contribution

It introduces a new optimal measurement framework for maximum-confidence discrimination of mixed quantum states with explicit conditions and solutions.

Findings

Derived necessary and sufficient optimality conditions.

Applied results to symmetric mixed states with analytical solutions.

Demonstrated effectiveness on symmetric pure and mixed states.

Abstract

We study an optimized measurement which discriminates N mixed quantum states occurring with given prior robabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the overall probability of inconclusive outcomes as small as possible. It corresponds to optimum unambiguous discrimination when for each outcome the confidence is equal to unity. Necessary and sufficient optimality conditions are derived and general properties of the optimum measurement are obtained. The results are applied to the optimized maximum-confidence discrimination of N equiprobable symmetric mixed states. Analytical solutions are presented for a number of examples, including the discrimination of N symmetric pure states spanning a d-dimensional Hilbert space (d \leq N) and the discrimination of N symmetric mixed qubit states.