The Minimum Size of Qubit Unextendible Product Bases
Quantum Physics
2013-11-15 v1
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.
Keywords
Cite
@article{arxiv.1302.1604,
title = {The Minimum Size of Qubit Unextendible Product Bases},
author = {Nathaniel Johnston},
journal= {arXiv preprint arXiv:1302.1604},
year = {2013}
}
Comments
13 pages, 13 figures