Mutually Unbiased Bases and Semi-definite Programming
Quantum Physics
2011-02-10 v1 Mathematical Physics
math.MP
Optimization and Control
Abstract
A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and on Grobner bases. A third algorithmic approach is presented: the non-existence of more than three mutually unbiased bases in composite dimensions can be decided by a global optimization method known as semidefinite programming. The method is used to confirm that the spectral matrix cannot be part of a complete set of seven mutually unbiased bases in dimension six.
Cite
@article{arxiv.1006.0093,
title = {Mutually Unbiased Bases and Semi-definite Programming},
author = {Stephen Brierley and Stefan Weigert},
journal= {arXiv preprint arXiv:1006.0093},
year = {2011}
}
Comments
11 pages,