Condition for unambiguous state discrimination with local operations and classical communication

We obtain a necessary and sufficient condition for a finite set of states of a finite dimensional multiparticle quantum system to be amenable to unambiguous discrimination using local operations and classical communication. This condition is valid for states which may be be mixed, entangled or both. When the support of the set of states is the entire multiparticle Hilbert space, this condition is found to have an intriguing connection with the theory of entanglement witnesses.