Mutually Unbiased Bases for Continuous Variables
Quantum Physics
2009-11-13 v2
Abstract
The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N = 2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.
Keywords
Cite
@article{arxiv.0802.0394,
title = {Mutually Unbiased Bases for Continuous Variables},
author = {Stefan Weigert and Michael Wilkinson},
journal= {arXiv preprint arXiv:0802.0394},
year = {2009}
}
Comments
5 pages, no figures, revised to be identical to published text