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Abstract
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Using the equality form of the necessary and sufficient conditions introduced in Jafarizadeh (Phys Rev A 84:012102 (9 pp), 2011), minimum error discrimination between states of the two sets of equiprobable similarity transformed quantum
qudit states is investigated. In the case that the unitary operators describing the similarity transformations are generating sets of two irreducible representations and the
states fulfill a certain constraint, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form.
In the cases that they are generating sets of reducible representations, there exist no
closed-form formula in general, but the procedure can be applied properly in each case
provided that the states obey some constraints. Finally, we give the maximum success
probability of discrimination and optimal measurement operators for some important
examples of mixed quantum states, such as generalized Bloch sphere m-qubit states,
qubit states and their three special cases.
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