%0 Journal Article
%A Capel, Ángela
%A Lucia, Angelo
%A Pérez García, David
%T Quantum conditional relative entropy and quasi-factorization of the relative entropy
%D 2018
%@ 1751-8121
%U https://hdl.handle.net/20.500.14352/93636
%X The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing condition in the Gibbs measure associated to their dynamics, via a quasi-factorization of the entropy in terms of the conditional entropy in some sub-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For that, we define the quantum conditional relative entropy and prove several quasi-factorization results for it. As an illustration of their potential, we use one of them to obtain a positive log-Sobolev constant for the heat-bath dynamics with product fixed point.
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