Unextendible product bases, uncompletable product bases and bound entanglement

Journal article (2003)

Authors

David P. Divincenzo IBM Thomas J. Watson Research Centre

Tal Mor University of California

Peter W. Shor AT and T Research

John A. Smolin IBM Thomas J. Watson Research Centre

B.M. Terhal IBM Thomas J. Watson Research Centre

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External organisation

Hilbert Space High Dimension Entangle State Product State Complete Characterization

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Published Date

2003

Language

English

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Abstract

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.