Quantum optimal transport is cheaper
Analysis of PDEs
2021-03-19 v4 Information Theory
Mathematical Physics
math.IT
math.MP
Probability
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.
Cite
@article{arxiv.1908.01829,
title = {Quantum optimal transport is cheaper},
author = {François Golse and Emanuele Caglioti and Thierry Paul},
journal= {arXiv preprint arXiv:1908.01829},
year = {2021}
}