Complete log-Sobolev inequalities

Li Gao (University of Houston)

Thursday 14th October 16:00-17:00 Online

Abstract

Logarithmic Sobolev inequalities (LSI) were first introduced by L. Gross in 70s, and later found rich connections to geometry, probability, optimal transport as well as information theory. In recent years, logarithmic Sobolev inequalities for quantum Markov semigroups attracted a lot of attentions in quantum information theory and quantum many-body system. For classical Markov semigroups, an important advantage of log-Sobolev inequalities is the tensorization property that if two semigroups satisfy LSI, so does their tensor product semigroup. Nevertheless, tensorization property is wild open in the quantum cases and fails for non-primitive semigroups. In this talk, I'll present some recent progresses on tensor stable log-Sobelev inequalities for finite dimensional quantum Markov semigroups. This talk is based on a joint work with Cambyse Rouzé.

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