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We study an optimized measurement that discriminates two mixed quantum stateswith maximum confidence for each conclusive result, thereby keeping the overallprobability of inconclusive results as small as possible. When the rank of thedetection operators associated with the two different conclusive outcomes doesnot exceed unity we obtain a general solution. As an application, we considerthe discrimination of two mixed qubit states. Moreover, for the case ofhigher-rank detection operators we give a solution for particular states. Therelation of the optimized measurement to other discrimination schemes is alsodiscussed.

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