Foundation of Quantum Optimal Transport and Applications
Abstract
Quantum optimal transportation seeks an operator which minimizes the total cost of transporting a quantum state to another state, under some constraints that should be satisfied during transportation. We formulate this issue by extending the Monge-Kantorovich problem, which is a classical optimal transportation theory, and present some applications. As examples, we address quantum walk, quantum automata and quantum games from a viewpoint of optimal transportation. Moreover we explicitly show the folk theorem of the prisoners' dilemma, which claims mutual cooperation can be an equilibrium of the repeated game. A series of examples would show generic and practical advantages of the abstract quantum optimal transportation theory.
Keywords
Cite
@article{arxiv.1906.09817,
title = {Foundation of Quantum Optimal Transport and Applications},
author = {Kazuki Ikeda},
journal= {arXiv preprint arXiv:1906.09817},
year = {2024}
}
Comments
16 pages, 1 figure