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We study an optimum measurement for quantum state discrimination, whichmaximizes the probability of correct results when the probability ofinconclusive results is fixed at a given value. The measurement describesminimum-error discrimination if this value is zero, while under certainconditions it corresponds to optimized maximum-confidence discrimination, or tooptimum unambiguous discrimination, respectively, when the fixed value reachesa definite minimum. Using operator conditions that determine the optimummeasurement, we derive analytical solutions for the discrimination of two mixedqubit states, including the case of two pure states occurring with arbitraryprior probabilities, and for the discrimination of N symmetric states, bothpure and mixed. We also consider a case where the given density operatorsresolve the identity operator, and we specify the optimality conditions for thecase of partially symmetric states. Moreover, we show that from the completesolution for arbitrary values of the fixed rate of inconclusive results one canalways obtain the optimum measurement in another strategy where the error rateis fixed, and vice versa.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Optimal state discrimination with a fixed rate of inconclusive results:  Analytical solutions and relation to state discrimination with a fixed error  rate