Quantum Conditional Relative Entropy and Quasi-Factorization of the relative entropy
Duration: 40 mins 19 secs
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About this item
| Description: |
Capel, A
Friday 27th July 2018 - 11:45 to 12:30 |
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| Created: | 2018-07-30 11:32 |
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| Collection: | Mathematical Challenges in Quantum Information |
| Publisher: | Isaac Newton Institute |
| Copyright: | Capel, A |
| Language: | eng (English) |
| Abstract: | 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--algebras.
In this work we analyze analogous quasi-factorization 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 them to obtain a positive log-Sobolev constant for the heat-bath dynamics with product fixed point. |
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