Optimal transport pseudometrics for quantum and classical densities
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.
scientific article; zbMATH DE number 7489495
scientific article