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Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

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arxiv 2102.04434 v1 pith:2M4X2WPT submitted 2021-02-08 quant-ph math.OA

Geometric Approach Towards Complete Logarithmic Sobolev Inequalities

classification quant-ph math.OA
keywords approachestimatescarnot-caratheodorycompactcompletedecaydesignsdiameter
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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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