Triangle inequalities of quantum Wasserstein distances on noncommutative tori

Triangle inequalities of quantum Wasserstein distances on noncommutative tori

Fu, Jinshi (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Delft Institute of Applied Mathematics)

Caspers, M.P.T. (mentor)
de Laat, D. (graduation committee)
Zegers, S.E. (graduation committee)

Delft University of Technology

Applied Mathematics

2024-06-06

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.

optimal transport
Wasserstein distance
noncommutative tori
triangle inequality
noncommutative Lp-spaces
spectral decomposition

http://resolver.tudelft.nl/uuid:862f0b68-c4f0-4bea-a07c-71fe89cba942

Student theses

master thesis

© 2024 Jinshi Fu