Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems

E.A. Carlen, J. Maas, (2018).

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Abstract
We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.
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2018-11-12
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Cite this

Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. 2018.
Carlen, E. A., & Maas, J. (2018). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. ArXiv.
Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” ArXiv, 2018.
E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems.” ArXiv, 2018.
Carlen EA, Maas J. 2018. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems.
Carlen, Eric A., and Jan Maas. Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems. ArXiv, 2018.

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