Quantum optimal transport is cheaper

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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Submitted on : Wednesday, July 31, 2019 - 7:48:49 PM
Last modification on : Saturday, August 24, 2019 - 1:12:14 AM

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  • HAL Id : hal-02214344, version 1
  • ARXIV : 1908.01829

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Emanuele Caglioti, François Golse, Thierry Paul. Quantum optimal transport is cheaper. 2019. ⟨hal-02214344v1⟩

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