Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian Distributions and Phase Space Weyl--Heisenberg Frames   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.

1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an