Mutually unbiased bases in dimension six: The four most distant bases
Quantum Physics
2015-05-27 v1
Abstract
We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in dimension six. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically-found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.
Keywords
Cite
@article{arxiv.1103.1025,
title = {Mutually unbiased bases in dimension six: The four most distant bases},
author = {Philippe Raynal and Xin Lü and Berthold-Georg Englert},
journal= {arXiv preprint arXiv:1103.1025},
year = {2015}
}
Comments
10 pages, 2 figures, 1 table