Quantum optimal transport is cheaper

Emanuele Caglioti (1) , François Golse (2) , Thierry Paul (3)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Domaines: Théorie de l'information [cs.IT]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

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