Optimal transport pseudometrics for quantum and classical densities
type: Item
instance of: scholarly article
title: Optimal transport pseudometrics for quantum and classical densities
zbMATH Open document ID: 1485.49053
author: François Golse
author: Thierry Paul
published in: Journal of Functional Analysis
publication date: 2022-03-15T00:00:00Z
review text: The authors develop their previous work by providing variants of the triangle inequality for the quantum analogues of the Wasserstein metric of exponent \(2\) recently introduced by them (with other coauthors) in order to compare two density operators, and a phase space probability measure and a density operator, respectively. Various technical preliminary results, some of interest of their own, are also proven, an analogue of the Kantorovich duality being employed for defining an analogue of the Brenier transport map for the functional previously defined by the authors in order to compare a phase space probability measure and a density operator. Some results on quantum optimal transport and semiquantum Legendre transform close the paper.
reviewed by: Sorin-Mihai Grad
Mathematics Subject Classification ID: 49Q22
Mathematics Subject Classification ID: 81Q20
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 7489495
zbMATH Keywords: quantum Wasserstein metric
zbMATH Keywords: triangle inequality
zbMATH Keywords: Kantorovich duality
zbMATH Keywords: optimal transport
MaRDI profile type: Publication
full work available at URL: j.jfa.2022.109417
OpenAlex ID: W4210651181
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DOI: 10.1016/J.JFA.2022.109417
description: scientific article; zbMATH DE number 7489495