  We discuss the problem of designing unambiguous programmable discriminators
for any n unknown quantum states in an m-dimensional Hilbert space. The
discriminator is a fixed measurement that has two kinds of input registers: the
program registers and the data register. The quantum state in the data register
is what users want to identify, which is confirmed to be among the n states in
program registers. The task of the discriminator is to tell the users which
state stored in the program registers is equivalent to that in the data
register. First, we give a necessary and sufficient condition for judging an
unambiguous programmable discriminator. Then, if $m=n$, we present an optimal
unambiguous programmable discriminator for them, in the sense of maximizing the
worst-case probability of success. Finally, we propose a universal unambiguous
programmable discriminator for arbitrary n quantum states.

Quantum Physics