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Explore new developments in quantum state learning and testing in this one-hour talk by Ryan O'Donnell from QuICS. Delve into efficient algorithms for quantum state tomography, the quantum equivalent of estimating probability distributions. Gain insights into the importance of distinguishing between total variation distance, Hellinger distance, KL divergence, and chi-squared divergence. Discover quantum-inspired enhancements to classical independence testing problems. Learn about collaborative research with Steven T. Flammia from Amazon, advancing the field of quantum information science.