A dual formula for the noncommutative transport distance
Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.
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Abstract
In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation.
Publishing Year
Date Published
2022-04-08
Journal Title
Journal of Statistical Physics
Acknowledgement
The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).
Open access funding provided by Institute of Science and Technology (IST Austria).
Volume
187
Issue
2
Article Number
19
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Cite this
Wirth M. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9
Wirth, M. (2022). A dual formula for the noncommutative transport distance. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9
Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9.
M. Wirth, “A dual formula for the noncommutative transport distance,” Journal of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022.
Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.
Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022, doi:10.1007/s10955-022-02911-9.
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