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arXiv · 1908.01829

Quantum optimal transport is cheaper

François Golse·Emanuele Caglioti·Thierry Paul
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Abstract

We compare bipartite (Euclidean) matching problems in classical and quantum mechanics. The quantum case is treated in terms of a quantum version of the Wasserstein distance introduced in [F. Golse, C. Mouhot, T. Paul, Commun. Math. Phys. 343 (2016), 165-205]. We show that the optimal quantum cost can be cheaper than the classical one. We treat in detail the case of two particles: the equal mass case leads to equal quantum and classical costs. Moreover, we show examples with different masses for which the quantum cost is strictly cheaper than the classical cost.

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François Golse, Emanuele Caglioti, Thierry Paul. 2019-08-01. Quantum optimal transport is cheaper. https://arxiv.org/abs/1908.01829

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