Quantum Optimal Transport with Convex Regularization

This conference talk presents Nataliia Monina's research on "Quantum Optimal Transport with Convex Regularization" delivered at IPAM's Optimal Transport for Density Operators workshop at UCLA. Explore how quantum optimal transport (QOT) extends classical transport theory to non-commutative settings, with a focus on duality results for QOT with general convex regularization. Learn about the existence and characterization of solutions for both primal and dual problems, following the proof strategy for strictly convex and differentiable cases before examining extensions to general convex regularization. The presentation also covers results on unbalanced QOT, including convergence of solutions as the marginal penalization parameter approaches infinity. This 31-minute talk, recorded March 31, 2025, is based on joint research with E. Caputo, A. Gerolin, and L. Portinale from the University of Ottawa.