Gergely Bunth (Rényi Institute): Wasserstein distances and divergences of order p

We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced by De Palma and Trevisan (2021), where quantum channels realize the transport. Relying on this general machinery, we introduce p-Wasserstein distances and divergences and study their relations to each other through the study of the possible set of p-cost operators in which they are defined. We briefly mention a triangle inequality for quadratic Wasserstein divergences under the sole assumption that an arbitrary one of the states involved is pure, which is a generalization of our previous result in this direction. The talk is based on the preprint https://arxiv.org/abs/2501.08066.