  There are two common settings in a quantum-state discrimination problem. One
is minimum-error discrimination where a wrong guess (error) is allowed and the
discrimination success probability is maximized. The other is unambiguous
discrimination where errors are not allowed but the inconclusive result "I
don't know" is possible. We investigate discrimination problem with a finite
margin imposed on the error probability. The two common settings correspond to
the error margins 1 and 0. For arbitrary error margin, we determine the optimal
discrimination probability for two pure states with equal occurrence
probabilities. We also consider the case where the states to be discriminated
are multipartite, and show that the optimal discrimination probability can be
achieved by local operations and classical communication.
