  We address a problem of identifying a given pure state with one of two
reference pure states, when no classical knowledge on the reference states is
given, but a certain number of copies of them are available. We assume the
input state is guaranteed to be either one of the two reference states. This
problem, which we call quantum pure state identification, is a natural
generalization of the standard state discrimination problem. The two reference
states are assumed to be independently distributed in a unitary invariant way
in the whole state space. We give a complete solution for the averaged maximal
success probability of this problem for an arbitrary number of copies of the
reference states in general dimension. It is explicitly shown that the obtained
mean identification probability approaches the mean discrimination probability
as the number of the reference copies goes to infinity.

Quantum Physics