Quantum optimal transport: an invitation-Reference-Cited by-同舟云学术

Quantum optimal transport: an invitation

Published:2024-08-09 Issue: Volume: Page:
ISSN:1972-6724
Container-title:Bollettino dell'Unione Matematica Italiana
language:en
Short-container-title:Boll Unione Mat Ital

Author:

Trevisan Dario^ORCID

Abstract

AbstractThe optimal mass transport problem was formulated centuries ago, but only recently there has been a surge in its applications, particularly in functional inequalities, geometry, stochastic analysis, and numerical solutions for partial differential equations. Quantum optimal transport aims to extend this success story to non-commutative systems, where density operators replace probability measures. This brief review paper aims to describe the latest approaches, highlighting their advantages, disadvantages, and open mathematical problems relevant to applications.

Funder

Ministero dell’Università e della Ricerca

Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s40574-024-00428-5.pdf

Reference53 articles.

1. Villani, C.: Optimal Transport: Old and New. Springer, Berlin (2009)

2. Peyré, G., Cuturi, M.: Computational optimal transport: With applications to data science. Found. Trends Mach. Learn. 11(5–6), 355–607 (2019)

3. Maas, J., Rademacher, S., Titkos, T., Virosztek, D. (eds.): Optimal Transport on Quantum Structures. Bolyai Society Mathematical Studies, Berlin (2024)

4. Ambrosio, L., Gigli, N., Savaré, G.: Gradient Flows: in Metric Spaces and in the Space of Probability Measures. Springer, Berlin (2005)

5. Santambrogio, F.: Optimal transport for applied mathematicians. Birkäuser 55(58–63), 94 (2015)