Unextendible Product Bases and Bound Entanglement
Quantum Physics
2009-10-31 v2
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 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.
Cite
@article{arxiv.quant-ph/9808030,
title = {Unextendible Product Bases and Bound Entanglement},
author = {C. H. Bennett and D. P. DiVincenzo and T. Mor and P. W. Shor and J. A. Smolin and B. M. Terhal},
journal= {arXiv preprint arXiv:quant-ph/9808030},
year = {2009}
}
Comments
4 pages RevTex + 1 eps fig. This is version 2 with many changes and simplifications, and an additional author