Quasi-factorization of the quantum relative entropy

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• Ángela Capel Cuevas (ICMAT)
• Thursday 26 April 2018, 14:15-15:15
• MR21, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Johannes Bausch.

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 some conditional entropies.

In this talk, we analyze analogous quasi-factorization results in the quantum case. For that, we define 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.

This is joint work with Angelo Lucia (U. Copenhagen) and David Pérez-García (U. Complutense de Madrid).

This talk is part of the CQIF Seminar series.

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