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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.
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Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2015
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On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces
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Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
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Geometric inequalities from phase space translations
Stefan Huber, Robert König, and Anna Vershynina · 2017
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An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models
Markus Mittnenzweig and Alexander Mielke · 2017
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Complete Logarithmic Sobolev Inequalities via Ricci Curvature Bounded Below II
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Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems
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Relating Relative Entropy, Optimal Transport and Fisher Information: A Quantum HWI Inequality
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Complete Sobolev Type Inequalities
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