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We analyze the optimal unambiguous discrimination of two arbitrary mixedquantum states. We show that the optimal measurement is unique and we presentthis optimal measurement for the case where the rank of the density operator ofone of the states is at most 2 ("solution in 4 dimensions"). The solution isillustrated by some examples. The optimality conditions proved by Eldar et al.[Phys. Rev. A 69, 062318 (2004)] are simplified to an operational form. As anapplication we present optimality conditions for the measurement, when only oneof the two states is detected. The current status of optimal unambiguous statediscrimination is summarized via a general strategy.

Structural approach to unambiguous discrimination of two mixed quantum states