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- W4287556554 abstract "We show how one can obtain a class of quadratic Wasserstein metrics, that is to say, Wasserstein metrics of order 2, on the set of faithful normal states of a von Neumann algebra $A$, via transport plans, rather than through a dynamical approach. Two key points to make this work, are a suitable formulation of the cost of transport arising from Tomita-Takesaki theory and relative tensor products of bimodules (or correspondences in the sense of Connes). The triangle inequality, symmetry and $W_{2}(mu,mu)=0$ all work quite generally, but to show that $W_{2}(mu,nu)=0$ implies $mu=nu$, we need to assume that $A$ is finitely generated." @default.
- W4287556554 created "2022-07-25" @default.
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- W4287556554 date "2020-12-07" @default.
- W4287556554 modified "2023-10-17" @default.
- W4287556554 title "Quadratic Wasserstein metrics for von Neumann algebras via transport plans" @default.
- W4287556554 doi "https://doi.org/10.48550/arxiv.2012.03564" @default.
- W4287556554 hasPublicationYear "2020" @default.
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