eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2013-11-13
93
105
10.4230/LIPIcs.TQC.2013.93
article
The Minimum Size of Qubit Unextendible Product Bases
Johnston, Nathaniel
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol022-tqc2013/LIPIcs.TQC.2013.93/LIPIcs.TQC.2013.93.pdf
unextendible product basis; quantum entanglement; graph factorization