• Corpus ID: 252519642

Complete order and relative entropy decay rates

  title={Complete order and relative entropy decay rates},
  author={Li Gao and Marius Junge and Nicholas Laracuente and Haojian Li},
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… 
1 Citations

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We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite