  We study how to unambiguously identify a given quantum pure state with one of
the two reference pure states when no classical knowledge on the reference
states is given but a certain number of copies of each reference quantum state
are presented. By the unambiguous identification, we mean that we are not
allowed to make a mistake but our measurement can produce an inconclusive
result. Assuming the two reference states are independently distributed over
the whole pure state space in a unitary invariant way, we determine the optimal
mean success probability for an arbitrary number of copies of the reference
states and a general dimension of the state space. It is explicitly shown that
the obtained optimal mean success probability asymptotically approaches that of
the unambiguous discrimination as the number of the copies of the reference
states increases.
