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Wasserstein Distances on Quantum Structures: an Overview
Emily Beatty
https://arxiv.org/abs/2506.09794 https://arxiv.org/pdf/2506.097…

Wasserstein Distances on Quantum Structures: an Overview
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal transport tools from probability measures to quantum states has shown great promise over the last few years, particularly in the development of the theory of Wasserstein-style distances and divergences between quantum states. Such distances have already led to a…