Unextendible Product Bases and Bound Entanglement

Charles H. Bennett, David P. Di Vincenzo, Tal Mor, Peter W. Shor, John A. Smolin, Barbara M. Terhal

Research output: Contribution to journalArticleScientificpeer-review

535 Citations (Scopus)


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 2×2×2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e., all three corresponding 2×4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local positive operator valued measurements and classical communication.

Original languageEnglish
Pages (from-to)5385-5388
Number of pages4
JournalPhysical Review Letters
Issue number26
Publication statusPublished - 1999
Externally publishedYes


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