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Watch a 51-minute lecture where Shmuel Friedland from the University of Illinois at Chicago presents "On Quantum Optimal Transport" at IPAM's Optimal Transport for Density Operators workshop at UCLA. Explore the quantum version of the Monge-Kantorovich optimal transport problem, focusing on how quantum transport cost related to a Hermitian cost matrix is minimized over bipartite coupling states with fixed reduced density matrices. Learn how the minimum quantum optimal transport cost can be computed using semidefinite programming and under what conditions it gives a semidistance. Discover the properties of the quantum Wasserstein-2 distance and examine a semi-analytic expression for quantum cost when using a projector on the antisymmetric subspace for single-qubit states. Investigate the quantum-to-classical transition of the Earth mover's distance, the concept of SWAP-fidelity compared to standard Uhlmann-Jozsa fidelity, and quantum optimal transport for general d-partite systems. Recorded March 31, 2025.
