Asymptotically optimal discrimination between pure quantum states

We consider the decision problem between a finite number of states of a finite quantum system, when an arbitrarily large number of copies of the system is available for measurements. We provide an upper bound on the exponential rate of decay of the averaged probability of rejecting the true state. It represents a generalized quantum Chernoff distance of a finite set of states. As our main result we prove that the bound is sharp in the case of pure states.