# Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement

```@article{DiVincenzo2003UnextendiblePB,
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={Communications in Mathematical Physics},
year={2003},
volume={238},
pages={379-410}
}```
• Published 22 August 1999
• Computer Science
• Communications in Mathematical Physics
AbstractWe 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…
277 Citations

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