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In this 50-minute lecture, explore Emily Beatty's presentation on "Order p quantum Wasserstein distances from couplings" delivered at IPAM's Optimal Transport for Density Operators workshop at UCLA. Delve into a novel definition of quantum Wasserstein distances that overcomes limitations of existing approaches by utilizing the coupling method and metrics applicable to pure states. Discover how this definition exhibits properties expected of an optimal quantum version of the Wasserstein distance while integrating familiar quantum information theory metrics like trace distance. Learn about the analysis of this metric in random quantum states, phase transitions in complexity of subsystems, derivation of circuit lower bounds, and applications to hypercontractive inequalities for quantum channels without faithful fixed points. Understand how this distance definition is well-suited for quantum Wasserstein generative adversarial networks. Recorded April 2, 2025, this talk by Emily Beatty from École Normale Supérieure de Lyon provides valuable insights into extending optimal transport frameworks to quantum states.
