Numerical evidence for the maximum number of mutually unbiased bases in dimension six
Quantum Physics
2009-11-13 v2
Abstract
The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper we move away from the traditional analytic approach and use a numerical approach to attempt to determine this number. We numerically minimise a non-negative function of a set of N+1 orthonormal bases in dimension d which only evaluates to zero if the bases are mutually unbiased. As a result we find strong evidence that (as has been conjectured elsewhere) there are no more than three mutually unbiased bases in dimension six.
Keywords
Cite
@article{arxiv.quant-ph/0701122,
title = {Numerical evidence for the maximum number of mutually unbiased bases in dimension six},
author = {Paul Butterley and William Hall},
journal= {arXiv preprint arXiv:quant-ph/0701122},
year = {2009}
}
Comments
4 pages, 2 figures, some minor changes made