Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
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.
Keywords
Cite
@article{arxiv.quant-ph/9908070,
title = {Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement},
author = {David P. DiVincenzo and Tal Mor and Peter W. Shor and John A. Smolin and Barbara M. Terhal},
journal= {arXiv preprint arXiv:quant-ph/9908070},
year = {2007}
}
Comments
24 pages RevTex, 15 figures; appendix removed, several small corrections, to appear in Comm. Math. Phys