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Explore a 43-minute lecture by Therese Landry from the University of California, Santa Barbara, presenting "Quantum Wasserstein Distance on the Quantum Permutation Group" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Recorded on May 23, 2025, this talk investigates quantum compact groups supporting quantum metric space structure, with a focus on defining an analog of the Hamming metric on the quantum permutation group S+n. Learn how the construction of this quantum metric builds on the work of Biane and Voiculescu, and discover the associated quantum 1-Wasserstein distance on the tracial state space of C(S+n). The presentation covers joint research with David Jekel and Anshu Nirbay, offering insights into advanced mathematical concepts at the intersection of quantum theory and optimal transport.
