Triangle inequalities of quantum Wasserstein distances on noncommutative tori

Master thesis (2024)

Authors

J. Fu Electrical Engineering, Mathematics and Computer Science

Contributors

M.P.T. Caspers Analysis - EEMCS (mentor)
D. de Laat Discrete Mathematics and Optimization - EEMCS (graduation committee member)
S.E. Zegers Analysis - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
More Info
expand_more

Published Date

06-06-2024

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In 2022, Golse and Paul defined a pseudometric for quantum optimal transport that extends the classical Wasserstein distance. They proved that the pseudometric satisfies the triangle inequality in certain cases. This thesis reviews their proof in the case where the middle point is a classical density. Motivated by that proof, we formulate the optimal transport problem and propose the quantum Wasserstein distance on the noncommutative 2-torus. This thesis also proves that the proposed quantum Wasserstein distance satisfies the triangle inequality in the case where the middle point is a classical density on the 2-torus.