Unambiguous discrimination of linearly independent pure quantum states: Optimal average probability of success

We consider the problem of unambiguous (error-free) discrimination of $N$ linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive an upper bound on the optimal average probability of success using a result on optimal local conversion between two bipartite pure states. We prove that for any $N\ge 2$ an optimal measurement in general saturates our bound. In the exceptional cases we show that the bound is tight, but not always optimal.