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SUMMARY:Quantum Conditional Relative Entropy and Quasi-Factorization of th
 e relative entropy - Ángela Capel (ICMAT)
DTSTART:20180727T104500Z
DTEND:20180727T113000Z
UID:TALK108427@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>  The existence of a positive log-Sobolev constant impli
 es a bound on the  <span>mixing time of a quantum dissipative evolution un
 der the Markov approximation. For classical spin systems\, such constant w
 as proven to exist\, under the assumption of a mixing condition in the Gib
 bs measure associated to their dynamics\, via a quasi-factorization of the
  entropy in terms of the conditional entropy in some sub--algebras.<br></s
 pan></span><br> In this work we analyze analogous quasi-factorization resu
 lts in the quantum case. For that\, we dene the quantum conditional relati
 ve entropy and prove several quasi-factorization results for it. As an ill
 ustration of their potential\, we use one of them to obtain a positive log
 -Sobolev constant for the heat-bath dynamics with product fixed point.  <b
 r><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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