Exponential Decay of Matrix $\Phi$-Entropies on Markov Semigroups with Applications to Dynamical Evolutions of Quantum Ensembles

Hao-Chung Cheng, Min-Hsiu Hsieh, Marco Tomamichel

In the study of Markovian processes, one of the principal achievements is the equivalence between the $\Phi$-Sobolev inequalities and an exponential decrease of the $\Phi$-entropies. In…