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