Bound on local unambiguous discrimination between multipartite quantum states

We investigate the upper bound on unambiguous discrimination by local operations and classical communication. We demonstrate that any set of linearly independent multipartite pure quantum states can be locally unambiguously discriminated if the number of states in the set is no more than , where the space spanned by the set can be expressed in the irreducible form and is the optimal local dimension of the party. That is, is an upper bound. We also show that it is tight, namely there exists a set of states, in which at least one of the states cannot be locally unambiguously discriminated. Our result gives the reason why the multiqubit system is the only exception when any three quantum states are locally unambiguously distinguished.