Unextendible Product Bases and Bound Entanglement

Journal article (1999)

Authors

Charles H. Bennett IBM Thomas J. Watson Research Centre
D.P. di Vincenzo IBM Thomas J. Watson Research Centre
Tal Mor University of California, Université de Montréal
Peter W. Shor AT and T Research
John A. Smolin IBM Thomas J. Watson Research Centre
B.M. Terhal Universiteit van Amsterdam, Centrum Wiskunde & Informatica (CWI)
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Published Date

1999

Language

English

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Abstract

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.