Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

• URL: http://arxiv.org/abs/2102.04434v1
• Date: Mon, 8 Feb 2021 18:48:15 GMT
• Title: Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
• Authors: Li Gao, Marius Junge, Haojian Li
• Abstract summary: 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. Our approach relies on the transference principle, the existence of $t$-designs, and the sub-Riemanian diameter of compact Lie groups and implies estimates for the spectral gap.
• Score: 15.86478274881752
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 $t$-designs, and the sub-Riemannian diameter of compact Lie groups and implies estimates for the spectral gap.

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