Optimal conclusive discrimination of two nonorthogonal pure product multipartite states through local operations

We consider one copy of a quantum system prepared in one of two nonorthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols that achieve optimal conclusive discrimination by means of local operations and classical communications as good as by global measurements. Also, we show a protocol that minimizes the average number of local operations, Our result implies that two pure product multipartite states might not have the nonlocal property although more than two can have.