Quantum conditional relative entropy and quasi-factorization of the relative entropy
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 484001 |
Tidsskrift | Journal of Physics A: Mathematical and Theoretical |
Vol/bind | 51 |
Udgave nummer | 48 |
Antal sider | 41 |
ISSN | 1751-8113 |
DOI | |
Status | Udgivet - 2018 |
Links
- http://arxiv.org/pdf/1804.09525v1
Indsendt manuskript
ID: 198519028