We consider one copy of a quantum system prepared in one of two
non-orthogonal pure product states of multipartite distributed among separated
parties. We show that there exist protocols which obtain optimal probability in
the sense of conclusive discrimination by means of local operations and
classical communications(LOCC) as good as by global operations. Also, we show a
protocol which minimezes the average number of local operations. Our result
implies that two product pure multipartite states might not have the non-local
property though more than two can have.Comment: revtex, 3 pages, no figur
