  In this paper, we consider the LOCC distinguishability of product states. We
employ polygons to analyze orthogonal product states in any system to show that
with LOCC protocols, to distinguish seven orthogonal product states, one can
exclude four states via a single copy. In bipartite systems, this result
implies that N orthogonal product states are LOCC distinguishable if $\left
\lceil \frac{N}{4} \right \rceil$ copies are allowed, where $\left \lceil
l\right \rceil$ for a real number $l$ means the smallest integer not less than
$l$. In multipartite systems, this result implies that N orthogonal product
states are LOCC distinguishable if $\left \lceil \frac{N}{4}\right \rceil + 1$
copies are allowed. We also give a theorem to show how many states can be
excluded via a single copy if we are distinguishing n orthogonal product states
by LOCC protocols in a bipartite system. Not like previous results, our result
is a general result for any set of orthogonal product states in any system.
