Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
Quantum Physics
2021-02-09 v1 Operator Algebras
Abstract
In this paper, we use the Carnot-Caratheodory distance from sub-Riemanian geometry to prove entropy decay estimates for all finite dimensional symmetric quantum Markov semigroups. This estimate is independent of the environment size and hence stable under tensorization. Our approach relies on the transference principle, the existence of -designs, and the sub-Riemannian diameter of compact Lie groups and implies estimates for the spectral gap.
Cite
@article{arxiv.2102.04434,
title = {Geometric Approach Towards Complete Logarithmic Sobolev Inequalities},
author = {Li Gao and Marius Junge and Haojian Li},
journal= {arXiv preprint arXiv:2102.04434},
year = {2021}
}
Comments
12 pages. A preliminary version. Comments are welcome!