Unextendible Product Bases and Bound Entanglement

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Unextendible Product Bases and Bound Entanglement

Journal Article (1999)

Author(s)

Charles H. Bennett (IBM Thomas J. Watson Research Centre)

David P. Di Vincenzo (IBM Thomas J. Watson Research Centre)

Tal Mor (Université de Montréal, University of California)

Peter W. Shor (AT and T Research)

John A. Smolin (IBM Thomas J. Watson Research Centre)

Barbara M. Terhal (Centrum Wiskunde & Informatica (CWI), Universiteit van Amsterdam)

Affiliation

External organisation

DOI related publication

https://doi.org/10.1103/PhysRevLett.82.5385 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:8b1cace7-338b-41e4-a358-25608dfde954

More Info

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Publication Year

1999

Language

English

Affiliation

External organisation

Issue number

26

Volume number

82

Pages (from-to)

5385-5388

Downloads counter

208

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.