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Foundation of quantum optimal transport and applications

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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 an example, we address infinitely repeated quantum games and establish the folk theorem of the quantum prisoners’ dilemma, which claims mutual cooperation can be an equilibrium of the infinitely repeated quantum game. We also exhibit a series of examples which show generic and practical advantages of the abstract quantum optimal transportation theory.

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Acknowledgements

I thank Travis Humble for useful discussion about quantum computation and game theory. I came up with an idea of showing the folk theorem while I discussed with him. Also, I was benefited by discussing with Katsuya Hashino, Kin-ya Oda, and Satoshi Yamaguchi. The author was partly supported by Grant-in-Aid for JSPS Research Fellow, No. 19J11073.

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  1. Department of Physics, Osaka University, Toyonaka, Osaka, 5600043, Japan

    Kazuki Ikeda

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  1. Kazuki Ikeda
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Correspondence to Kazuki Ikeda.

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Ikeda, K. Foundation of quantum optimal transport and applications. Quantum Inf Process 19, 25 (2020). https://doi.org/10.1007/s11128-019-2519-8

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