  Research in non-orthogonal state discrimination has given rise to two
conventional optimal strategies: unambiguous discrimination (UD) and minimum
error (ME) discrimination. This paper explores the experimentally relevant
range of measurement strategies between the two, where the rate of inconclusive
results is minimized for a bounded-error rate. We first provide some
constraints on the problem that apply to generalized measurements (POVMs). We
then provide the theory for the optimal projective measurement (PVM) in this
range. Through analytical and numerical results we investigate this family of
projective, bounded-error strategies and compare it to the POVM family as well
as to experimental implementation of UD using POVMs. We also discuss a possible
application of these bounded-error strategies to quantum key distribution.
