[CvGmt News] [cvgmt seminar] Quantum Wasserstein "distances" and optimal transport

[ambrosio at sns.it]

Quantum Wasserstein "distances" and optimal transport
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http://cvgmt.sns.it/seminar/671/

Date: Tuesday, Dec 18, 2018

Time: 14:00

Place: Aula Fermi, Scuola Normale Superiore

Speaker: Thierry Paul



Abstract. 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.