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arXiv · 1906.09817

Foundation of Quantum Optimal Transport and Applications

Kazuki Ikeda
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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.

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Kazuki Ikeda. 2019-06-24. Foundation of Quantum Optimal Transport and Applications. https://doi.org/10.1007/s11128-019-2519-8

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