# 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} }

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…

## 270 Citations

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