  In this paper, we consider the problem of unambiguous discrimination between
a set of mixed quantum states. We first divide the density matrix of each mixed
state into two parts by the fact that it comes from ensemble of pure quantum
states. The first part will not contribute anything to the discrimination, the
second part has support space linearly independent to each other. Then the
problem we consider can be reduced to a problem in which the strategy of set
discrimination can be used in designing measurements to discriminate mixed
states unambiguously. We find a necessary and sufficient condition of
unambiguous mixed state discrimination, and also point out that searching the
optimal success probability of unambiguous discrimination is mathematically the
well-known semi-definite programming problem. A upper bound of the optimal
success probability is also presented. Finally, We generalize the concept of
set discrimination to mixed state and point out that the problem of
discriminating it unambiguously is equivalent to that of unambiguously
discriminating mixed states.
