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.
Quantum Optimal Transport is Cheaper / Caglioti, E.; Golse, F.; Paul, T.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - (2020). [10.1007/s10955-020-02571-7]
Quantum Optimal Transport is Cheaper
Caglioti E.
;Golse F.;Paul T.
2020
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. 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.| File | Dimensione | Formato | |
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Caglioti_Quantum-optimal-transport_2020.pdf
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