# Complete order and relative entropy decay rates

@inproceedings{Gao2022CompleteOA, title={Complete order and relative entropy decay rates}, author={Li Gao and Marius Junge and Nicholas Laracuente and Haojian Li}, year={2022} }

We prove that the complete modified log-Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its completely bounded mixing time. This implies that the complete modified log-Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension or index. The quantum version of a classical birth-death process shows that this bound is tight. Such an estimate is obtained for GNS-symmetric quantum Markov semigroups on general von Neumann algebras. As an…

## One Citation

### Asymptotic Equipartition Theorems in von Neumann algebras

- Mathematics, Computer Science
- 2022

The main technical contributions are to extend to the context of general von Neumann algebras a chain rule for quantum channels, as well as an additivity result for the channel relative entropy with a replacer channel.

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