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

Locality and nonlocality in quantum pure-state identification problems