  We present a complete characterization for the local distinguishability of
orthogonal $2\otimes 3$ pure states except for some special cases of three
states. Interestingly, we find there is a large class of four or three states
that are indistinguishable by local projective measurements and classical
communication (LPCC) can be perfectly distinguishable by LOCC. That indicates
the ability of LOCC for discriminating $2\otimes 3$ states is strictly more
powerful than that of LPCC, which is strikingly different from the case of
multi-qubit states. We also show that classical communication plays a crucial
role for local distinguishability by constructing a class of $m\otimes n$
states which require at least $2\min\{m,n\}-2$ rounds of classical
communication in order to achieve a perfect local discrimination.
