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arXiv · 1803.07538

Connes distance and optimal transport

Pierre Martinetti
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Abstract

We give a brief overview on the relation between Connes spectral distance in noncommutative geometry and the Wasserstein distance of order 1 in optimal transport. We first recall how these two distances coincide on the space of probability measures on a Riemannian manifold. Then we work out a simple example on a discrete space, showing that the spectral distance between arbitrary states does not coincide with the Wasserstein distance with cost the spectral distance between pure states.

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Pierre Martinetti. 2018-03-20. Connes distance and optimal transport. https://doi.org/10.1088/1742-6596%2F968%2F1%2F012007

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