2026-06-08T01:19:12Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/936362025-03-22T00:51:33Zcom_20.500.14352_14col_20.500.14352_15

Quantum conditional relative entropy and quasi-factorization of the relative entropy Capel, Ángela Lucia, Angelo Pérez García, David Conditional relative entropy Log-Sobolev inequality Quantum dissipative evolution Quasi-factorization of the relative entropy Quantum relative entropy Mixing time Física (Física) 22 Física 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. Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2024-01-17T14:05:52Z 2024-01-17T14:05:52Z 2018 journal article VoR https://hdl.handle.net/20.500.14352/93636 1751-8121 10.1088/1751-8121/aae4cf eng Capel Á, Lucia A and Pérez-García D 2018 Quantum conditional relative entropy and quasi-factorization of the relative entropy J. Phys. A: Math. Theor. 51 484001 restricted access application/pdf IOP Publishing