  We discuss the problem of designing an unambiguous programmable discriminator
for mixed quantum states. We prove that there does not exist such a universal
unambiguous programmable discriminator for mixed quantum states that has two
program registers and one data register. However, we find that we can use the
idea of programmable discriminator to unambiguously discriminate mixed quantum
states. The research shows that by using such an idea, when the success
probability for discrimination reaches the upper bound, the success probability
is better than what we do not use the idea to do, except for some special
cases.
