Calculus of Variations and Geometric Measure Theory

Quantum Wasserstein "distances" and optimal transport

Thierry Paul

created by ambrosio on 11 Dec 2018

18 dec 2018 -- 14:00   [open in google calendar]

Aula Fermi, Scuola Normale Superiore


I will define a quantum analogue to the Wasserstein distance of order two between density operators, namely positive trace one operators on Hilbert spaces. I will give first properties, in particular the link with usual Wasserstien distance between positive symbols of the quantum densities and show how they define a topology more adapted to the classical limit than the one defined by Schatten classes. Finally i will present recent results obtained with E. Caglioti and F. Golse concerning a quantum version of the Brenier optimal transport Theorem.