  We investigate generalized measurements, based on positive-operator-valued
measures, and von Neumann measurements for the unambiguous discrimination of
two mixed quantum states that occur with given prior probabilities. In
particular, we derive the conditions under which the failure probability of the
measurement can reach its absolute lower bound, proportional to the fidelity of
the states. The optimum measurement strategy yielding the fidelity bound of the
failure probability is explicitly determined for a number of cases. One example
involves two density operators of rank d that jointly span a 2d-dimensional
Hilbert space and are related in a special way. We also present an application
of the results to the problem of unambiguous quantum state comparison,
generalizing the optimum strategy for arbitrary prior probabilities of the
states.
