Workshop I: Optimal Transport for Density Operators: Theory and Numerics

Part of the Long Program Non-commutative Optimal Transport
March 31 - April 4, 2025


The quest to devise a non-commutative counterpart of the Monge-Kantorovich optimal transport theory began about thirty years ago with early proposals by A. Connes and D. Voiculescu. These early attempts focused mostly on the static Monge and Kantorovich formulations using duality theory. More recently, several formulations for the non-commutative counterpart of the Optimal Transport problem and Wasserstein distances have been proposed motivated by computational challenges and applications in Theoretical Chemistry and Quantum Physics.

The primary goal of this workshop is to foster collaborations and build bridges between three disjoint worlds of non-commutative (static) optimal transport, on both theoretical and computational aspects as well as potential developments in Quantum Physics and Electronic Structure Theory. This includes

  • Monge-Kantorovich formulation of Non-commutative Optimal Transport
  • Operator and Tensor Scaling
  • Quantum Optimal Transport between quantum channels and qubits
  • Optimal Transport Methods in Density Functional Theory
  • Developments in Reduced Density Matrix Functional Theory
  • (Static) Optimal Transport Theory for von-Neumann algebras


This workshop will include a poster session; a request for posters will be sent to registered participants before the workshop.

Organizing Committee

Eugene De Prince (Florida State University)
Augusto Gerolin (University of Ottawa)
Katarzyna Pernal (Politechnika Lodzka)
Dario Trevisan (Università di Pisa)