The Minimum Size of Qubit Unextendible Product Bases
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.
unextendible product basis; quantum entanglement; graph factorization
93-105
Regular Paper
Nathaniel
Johnston
Nathaniel Johnston
10.4230/LIPIcs.TQC.2013.93
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode