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. 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.

中文翻译：

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量子最优传输更便宜

我们比较经典力学和量子力学中的二部（欧几里得）匹配问题。量子情况是根据 Wasserstein 距离的量子版本来处理的。我们表明，最优的量子成本可以比经典的更便宜。我们详细讨论了两个粒子的情况：质量相等的情况导致量子成本和经典成本相等。此外，我们展示了具有不同质量的示例，其量子成本严格低于经典成本。