Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results

TL;DR

This paper develops an optimized quantum measurement strategy to distinguish two mixed quantum states with maximum confidence and minimal inconclusive results, providing general solutions and specific cases for qubits.

Contribution

It introduces a new optimized measurement approach for quantum state discrimination that minimizes inconclusive outcomes while maximizing confidence, including solutions for special cases.

Findings

Derived a general solution for rank-one detection operators.

Provided specific solutions for mixed qubit states.

Discussed the relation to other quantum discrimination schemes.

Abstract

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the detection operators associated with the two different conclusive outcomes does not exceed unity we obtain a general solution. As an application, we consider the discrimination of two mixed qubit states. Moreover, for the case of higher-rank detection operators we give a solution for particular states. The relation of the optimized measurement to other discrimination schemes is also discussed.