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DOI: 10.4230/LIPIcs.TQC.2013.93
URN: urn:nbn:de:0030-drops-43173
URL: https://drops.dagstuhl.de/opus/volltexte/2013/4317/
Johnston, Nathaniel
The Minimum Size of Qubit Unextendible Product Bases
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Abstract
We investigate the problem of constructing unextendible product bases in the qubit case - that is, when each local dimension equals 2. The cardinality of the smallest unextendible product basis is known in all qubit cases except when the number of parties is a multiple of 4 greater than 4 itself. We construct small unextendible product bases in all of the remaining open cases, and we use graph theory techniques to produce a computer-assisted proof that our constructions are indeed the smallest possible.
BibTeX - Entry
@InProceedings{johnston:LIPIcs:2013:4317,
author = {Nathaniel Johnston},
title = {{The Minimum Size of Qubit Unextendible Product Bases}},
booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
pages = {93--105},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-55-2},
ISSN = {1868-8969},
year = {2013},
volume = {22},
editor = {Simone Severini and Fernando Brandao},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2013/4317},
URN = {urn:nbn:de:0030-drops-43173},
doi = {10.4230/LIPIcs.TQC.2013.93},
annote = {Keywords: unextendible product basis; quantum entanglement; graph factorization}
}
| Keywords: | unextendible product basis; quantum entanglement; graph factorization | |
| Seminar: | 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) | |
| Issue date: | 2013 | |
| Date of publication: | 13.11.2013 |
