Foundation of Quantum Optimal Transport and Applications
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866917598193516544 |
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| author | Ikeda, Kazuki |
| author_facet | Ikeda, Kazuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_09817 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Foundation of Quantum Optimal Transport and Applications Ikeda, Kazuki Quantum Physics Mathematical Physics 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. |
| title | Foundation of Quantum Optimal Transport and Applications |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/1906.09817 |