Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
Quantum Physics
2008-10-21 v1
Abstract
We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the squares of the moduli of their scalar products are equal to zero, one, or 1/d. These sets will be called a MU constellation, and if four MU bases were to exist for d=6, they would give rise to 35 different MU constellations. Using a numerical minimisation procedure, we are able to identify only 18 of them in spite of extensive searches. The missing MU constellations provide the strongest numerical evidence so far that no seven MU bases exist in dimension six.
Keywords
Cite
@article{arxiv.0808.1614,
title = {Maximal Sets of Mutually Unbiased Quantum States in Dimension Six},
author = {Stephen Brierley and Stefan Weigert},
journal= {arXiv preprint arXiv:0808.1614},
year = {2008}
}
Comments
19 pages, 6 figures, 4 tables