Foundation of Quantum Optimal Transport and Applications

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 tr...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Ikeda, Kazuki
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 24.06.2019
Subjects
Game theory
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Physics - Quantum Physics
Prisoners
Transportation
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1906.09817