  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.
