How to differentiate between non-orthogonal states

We consider the following problem. A preparator prepares a collection of quantum systems so that every single system is prepared either in the state P or in the state Q, [P, Q] ≠ 0. An observer, knowing in advance that a single system state is either P or Q should find a way to tell, for as many as possible systems, in what state a single system has been prepared, P or Q. We show that a generalized measurement can be constructed which performs this task better than any combination of standard quantum measurements.