Proves hypercontractivity implies entropy contraction for quantum channels; derives modified log-Sobolev bounds for KMS-symmetric quantum Markov semigroups and establishes quantitative connections to approximate tensorization of relative entropy.

Proves hypercontractivity implies entropy contraction for quantum channels; derives modified log-Sobolev bounds for KMS-symmetric quantum Markov semigroups and establishes quantitative connections to approximate tensorization of relative entropy.