A Dual Formula for the Noncommutative Transport Distance

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 o...

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Detalles Bibliográficos
Autor principal: Wirth, Melchior
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8993752/
https://www.ncbi.nlm.nih.gov/pubmed/35509951
http://dx.doi.org/10.1007/s10955-022-02911-9
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author Wirth, Melchior
author_facet Wirth, Melchior
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description 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.
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spelling pubmed-89937522022-05-02 A Dual Formula for the Noncommutative Transport Distance Wirth, Melchior J Stat Phys Article 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. Springer US 2022-04-08 2022 /pmc/articles/PMC8993752/ /pubmed/35509951 http://dx.doi.org/10.1007/s10955-022-02911-9 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Wirth, Melchior
A Dual Formula for the Noncommutative Transport Distance
title A Dual Formula for the Noncommutative Transport Distance
title_full A Dual Formula for the Noncommutative Transport Distance
title_fullStr A Dual Formula for the Noncommutative Transport Distance
title_full_unstemmed A Dual Formula for the Noncommutative Transport Distance
title_short A Dual Formula for the Noncommutative Transport Distance
title_sort dual formula for the noncommutative transport distance
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8993752/
https://www.ncbi.nlm.nih.gov/pubmed/35509951
http://dx.doi.org/10.1007/s10955-022-02911-9
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