  An unextendible product basis (UPB) for a multipartite quantum system is an
incomplete orthogonal product basis whose complementary subspace contains no
product state. We give examples of UPBs, and show that the uniform mixed state
over the subspace complementary to any UPB is a bound entangled state. We
exhibit a tripartite 2x2x2 UPB whose complementary mixed state has tripartite
entanglement but no bipartite entanglement, i.e. all three corresponding 2x4
bipartite mixed states are unentangled. We show that members of a UPB are not
perfectly distinguishable by local POVMs and classical communication.
