Quantum Fourier Analysis
Operator Algebras
2021-06-30 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Physics
Abstract
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform , as a map between suitably defined spaces, leading to a new uncertainty principle for relative entropy. We cite several applications of the quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a new topological inequality, and we outline several open problems.
Cite
@article{arxiv.2002.03477,
title = {Quantum Fourier Analysis},
author = {Arthur Jaffe and Chunlan Jiang and Zhengwei Liu and Yunxiang Ren and Jinsong Wu},
journal= {arXiv preprint arXiv:2002.03477},
year = {2021}
}