Back to Search
Start Over
Quantum conditional relative entropy and quasi-factorization of the relative entropy
- Source :
- J. Phys. A: Math. Theor. 51 (2018) 484001
- Publication Year :
- 2018
-
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-$\sigma$-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.<br />Comment: v2: Final version, minor changes, 39 pages, 2 figures
- Subjects :
- Quantum Physics
Computer Science - Information Theory
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Phys. A: Math. Theor. 51 (2018) 484001
- Publication Type :
- Report
- Accession number :
- edsarx.1804.09525
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/1751-8121/aae4cf