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CATEGORIES:CQIF Seminar
SUMMARY:Quasi-factorization of the quantum relative entrop
y - Ángela Capel Cuevas (ICMAT)
DTSTART;TZID=Europe/London:20180426T141500
DTEND;TZID=Europe/London:20180426T151500
UID:TALK104668AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/104668
DESCRIPTION:The existence of a positive log-Sobolev constant i
mplies a bound on the mixing time of a quantum dis
sipative evolution under the Markov approximation.
For classical spin systems\, such constant was pr
oven to exist\, under the assumption of a mixing c
ondition in the Gibbs measure associated to their
dynamics\, via a quasi-factorization of the entrop
y in terms of some conditional entropies.\n\nIn th
is talk\, we analyze analogous quasi-factorization
results in the quantum case. For that\, we defin
e the quantum conditional relative entropy and pro
ve several quasi-factorization results for it. As
an illustration of their potential\, we use one of
them to obtain a positive log-Sobolev constant fo
r the heat-bath dynamics with product fixed point.
\n\nThis is joint work with Angelo Lucia (U. Copen
hagen) and David Pérez-García (U. Complutense de M
adrid).
LOCATION:MR21\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:Johannes Bausch
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