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Minimum-error discrimination between two sets of similarity-transformed quantum states

Using the necessary and sufficient conditions, minimum error discrimination among two sets of similarity transformed equiprobable quantum qudit states is investigated. In the case that the unitary operators are generating sets of two irreducible representations, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form. In the case of reducible representations, there exists no closed-form formula in general, but the procedure can be applied in each case accordingly. Finally, we give the maximum success probability of optimal discrimination for some important examples of mixed quantum states, such as qubit states together with three special cases and generalized Bloch sphere m-qubit states.