Gaussian Distributions and Phase Space Weyl--Heisenberg Frames
Mathematical Physics
2018-12-07 v2 math.MP
Abstract
Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation formulas for the expansion of a general Gaussian symbol in terms of elementary Gaussian functions. For this purpose we introduce the notion of a "phase space frame" associated with a Weyl-Heisenberg frame. Our results give explicit formulas for approximating general Gaussian symbols in phase space by phase space shifted standard Gaussians as well as explicit error estimates and the asymptotic behavior of the approximation.
Cite
@article{arxiv.1708.01551,
title = {Gaussian Distributions and Phase Space Weyl--Heisenberg Frames},
author = {Markus Faulhuber and Maurice A. de Gosson and David Rottensteiner},
journal= {arXiv preprint arXiv:1708.01551},
year = {2018}
}
Comments
20 pages, 1 figure, in press, to appear in: Applied and Computational Harmonic Analysis