It is known that the states in an unextendible product basis (UPB) cannot be
distinguished perfectly when the parties are restricted to local operations and
classical communication (LOCC). Previous discussions of such bases have left
open the following question: What entanglement resources are necessary and/or
sufficient for this task to be possible with LOCC? In this paper, I present
protocols which use entanglement more efficiently than teleportation to
distinguish certain classes of UPB's. The ideas underlying my approach to this
problem offer rather general insight into why entanglement is useful for such
tasks.Comment: Final, published version. Many revisions following very useful
suggestions of the referee have been added. In particular, Appendix A has
been completely rewritte
