dorsal/arxiv
View SchemaUnextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
| Authors | David P. DiVincenzo, Tal Mor, Peter W. Shor, John A. Smolin, Barbara M. Terhal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9908070 |
| URL | https://arxiv.org/abs/quant-ph/9908070 |
| DOI | 10.1007/s00220-003-0877-6 |
| Journal | Comm. Math. Phys. 238, pp. 379--410 (2003) |
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.
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"abstract": "We report new results and generalizations of our work on unextendible product\nbases (UPB), uncompletable product bases and bound entanglement. We present a\nnew construction for bound entangled states based on product bases which are\nonly completable in a locally extended Hilbert space. We introduce a very\nuseful representation of a product basis, an orthogonality graph. Using this\nrepresentation we give a complete characterization of unextendible product\nbases for two qutrits. We present several generalizations of UPBs to arbitrary\nhigh dimensions and multipartite systems. We present a sufficient condition for\nsets of orthogonal product states to be distinguishable by separable\nsuperoperators. We prove that bound entangled states cannot help increase the\ndistillable entanglement of a state beyond its regularized entanglement of\nformation assisted by bound entanglement.",
"arxiv_id": "quant-ph/9908070",
"authors": [
"David P. DiVincenzo",
"Tal Mor",
"Peter W. Shor",
"John A. Smolin",
"Barbara M. Terhal"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-003-0877-6",
"journal_ref": "Comm. Math. Phys. 238, pp. 379--410 (2003)",
"title": "Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement",
"url": "https://arxiv.org/abs/quant-ph/9908070"
},
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