• Corpus ID: 119151291

A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy

@article{Wirth2018ANT,
  title={A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy},
  author={Melchior Wirth},
  journal={arXiv: Operator Algebras},
  year={2018}
}
  • Melchior Wirth
  • Published 16 August 2018
  • Mathematics
  • arXiv: Operator Algebras
We study quantum Dirichlet forms and the associated symmetric quantum Markov semigroups on noncommutative $L^2$ spaces. It is known from the work of Cipriani and Sauvageot that these semigroups induce a first order differential calculus, and we use this differential calculus to define a noncommutative transport metric on the set of density matrices. This construction generalizes both the $L^2$-Wasserstein distance on a large class of metric spaces as well as the discrete transport distance… 

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