Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

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.

arXiv comment12 pages. A preliminary version. Comments are welcome!

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Cited by in corpus (2)

• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Quasi-factorization and Multiplicative Comparison of Subalgebra-Relative Entropy