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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Quantum Conditional Relative Entropy and Quasi-Fac
torization of the relative entropy - Ángela Capel
(ICMAT)
DTSTART;TZID=Europe/London:20180727T114500
DTEND;TZID=Europe/London:20180727T123000
UID:TALK108427AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108427
DESCRIPTION: The existence of a positive log-Sobolev co
nstant implies a bound on the mixing time o
f a quantum dissipative evolution under the Markov
approximation. For classical spin systems\, such
constant was proven to exist\, under the assumptio
n of a mixing condition in the Gibbs measure assoc
iated to their dynamics\, via a quasi-factorizatio
n of the entropy in terms of the conditional entro
py in some sub--algebras.

In
this work we analyze analogous quasi-factorizatio
n results in the quantum case. For that\, we dene
the quantum conditional relative entropy and prove
several quasi-factorization results for it. As an
illustration of their potential\, we use one of t
hem to obtain a positive log-Sobolev constant for
the heat-bath dynamics with product fixed point.

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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