# Curvature-dimension conditions for symmetric quantum Markov semigroups

@article{Wirth2021CurvaturedimensionCF, title={Curvature-dimension conditions for symmetric quantum Markov semigroups}, author={Melchior Wirth and Haonan Zhang}, journal={ArXiv}, year={2021}, volume={abs/2105.08303} }

Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension…

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