  We investigate a state discrimination problem which interpolates
minimum-error and unambiguous discrimination by introducing a margin for the
probability of error. We closely analyze discrimination of two pure states with
general occurrence probabilities. The optimal measurements are classified into
three types. One of the three types of measurement is optimal depending on
parameters (occurrence probabilities and error margin). We determine the three
domains in the parameter space and the optimal discrimination success
probability in each domain in a fully analytic form. It is also shown that when
the states to be discriminated are multipartite, the optimal success
probability can be attained by local operations and classical communication.
For discrimination of two mixed states, an upper bound of the optimal success
probability is obtained.
