2023/06/22 by Laurent Laflèche, Lafleche, Laurent · 2 citations
Mathematics · #46E35 (Secondary) #46N50 #49Q22 (Primary) 81Q05 #81Q20 #81S30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2306.12944
openalex publication_date 2023/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Several extensions of the classical optimal transport distances to the quantum setting have been proposed. In this paper, we investigate the pseudometrics introduced by Golse, Mouhot and Paul in [Commun Math Phys 343:165-205, 2016] and by Golse and Paul in [Arch Ration Mech Anal 223:57-94, 2017]. These pseudometrics serve as a quantum analogue of the Monge-Kantorovich-Wasserstein distances of order 2 on the phase space. We prove that they are comparable to negative Sobolev norms up to a small term due to a positive "self-distance" in the semiclassical approximation, which can be bounded above using the Wigner-Yanase skew information. This enables us to improve the known results in the context of the mean-field and semiclassical limits by requiring less regularity on the initial data.