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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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https://hal.archives-ouvertes.fr/hal-02214344
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Submitted on : Monday, May 4, 2020 - 10:15:37 AM
Last modification on : Thursday, December 3, 2020 - 4:55:43 PM

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  • HAL Id : hal-02214344, version 3
  • ARXIV : 1908.01829

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François Golse, Emanuele Caglioti, Thierry Paul. Quantum optimal transport is cheaper. Journal of Statistical Physics, 2020, 181 ((1),), pp.149-162. ⟨hal-02214344v3⟩

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