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We study the discrimination of N mixed quantum states in an optimalmeasurement that maximizes the probability of correct results while theprobability of inconclusive results is fixed at a given value. Afterconsidering the discrimination of N states in a d-dimensional Hilbert space, wefocus on the discrimination of qubit states. We develop a method to determinean optimal measurement for discriminating arbitrary qubit states, taking intoaccount that often the optimal measurement is not unique and the maximumprobability of correct results can be achieved by several differentmeasurements. Analytical results are derived for a number of examples, mostlyfor the discrimination between qubit states which possess a partial symmetry,but also for discriminating N equiprobable qubit states and for thedicrimination between a pure and a uniformly mixed state in d dimensions. Inthe special case where the fixed rate of inconclusive results is equal to zero,our method provides a treatment for the minimum-error discrimination ofarbitrary qubit states which differs from previous approaches.

Optimal measurements for the discrimination of quantum states with a fixed rate of inconclusive results