  We prove that the states secretly chosen from a mixed state set can be
perfectly discriminated if and only if these states are orthogonal. The
sufficient and necessary condition when nonorthogonal quantum mixed states can
be unambiguously discriminated is also presented. Furthermore, we derive a
series of lower bounds on the inconclusive probability of unambiguous
discrimination of states from a mixed state set with \textit{a prior}
probabilities.
