Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions
Functional Analysis
2018-07-25 v1 Information Theory
math.IT
Quantum Physics
Abstract
We prove a version of Talagrand's concentration inequality for subordinated sub-Laplacian on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.
Cite
@article{arxiv.1807.08838,
title = {Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions},
author = {Li Gao and Marius Junge and Nicolas LaRacuente},
journal= {arXiv preprint arXiv:1807.08838},
year = {2018}
}