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.

翻译：我们比较了古典力学和量子力学(Euclidean)的对称问题。量子学用[F. Golse, C. Mouhot, T. Paul, Commun. Math. Math. Phys. 343(2016), 165-205] 中引入的瓦瑟斯坦距离的量子版处理。我们表明,最佳量子成本可以比古典成本便宜。我们详细处理了两种粒子的情况:同等质量案例导致同等量量和经典成本。此外,我们用不同质量的例子展示了量子成本比经典成本更便宜。