Quantum conditional relative entropy and quasi-factorization of the relative entropy
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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-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For that, we define 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.
Original language | English |
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Article number | 484001 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 51 |
Issue number | 48 |
Number of pages | 41 |
ISSN | 1751-8113 |
DOIs | |
Publication status | Published - 2018 |
- conditional relative entropy, log-Sobolev inequality, mixing time, quantum dissipative evolution, quantum relative entropy, quasi-factorization of the relative entropy
Research areas
Links
- http://arxiv.org/pdf/1804.09525v1
Submitted manuscript
ID: 198519028