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Watch this 48-minute lecture where Rocco Duvenhage from the University of Pretoria presents an overview of the theory of Wasserstein distance between quantum dynamical systems with stationary faithful states. Recorded at IPAM's Dynamics of Density Operators Workshop at UCLA on April 29, 2025, the talk explores how transport plans can be used to measure distances between quantum systems. Learn how the dynamics given by the modular group associated to each state ensures symmetry, even when measuring Wasserstein distance between states themselves. The presentation emphasizes the role of the commutant of the observable algebra and related bimodule structure in Hilbert space representation theory, particularly in establishing the triangle inequality. Discover how Tomita-Takesaki modular theory of von Neumann algebras provides the structure and tools for this approach to quantum dynamics.
