RT Journal Article
T1 Quantum conditional relative entropy and quasi-factorization of the relative entropy
A1 Capel, Ángela
A1 Lucia, Angelo
A1 Pérez García, David
AB 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.
PB IOP Publishing
SN 1751-8121
YR 2018
FD 2018
LK https://hdl.handle.net/20.500.14352/93636
UL https://hdl.handle.net/20.500.14352/93636
LA eng
NO 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
DS Docta Complutense
RD 8 jun 2026