  Suppose we want to identify an input state with one of two unknown reference
states, where the input state is guaranteed to be equal to one of the reference
states. We assume that no classical knowledge of the reference states is given,
but a certain number of copies of them are available instead. Two reference
states are independently and randomly chosen from the state space in a unitary
invariant way. This is called the quantum state identification problem, and the
task is to optimize the mean identification success probability. In this paper,
we consider the case where each reference state is pure and bipartite, and
generally entangled. The question is whether the maximum mean identification
success probability can be attained by means of a local operations and
classical communication (LOCC) measurement scheme. Two types of identification
problems are considered when a single copy of each reference state is
available. We show that a LOCC scheme attains the globally achievable
identification probability in the minimum-error identification problem. In the
unambiguous identification problem, however, the maximal success probability by
means of LOCC is shown to be less than the globally achievable identification
probability.
