Foundation of quantum optimal transport and applications
Foundation of quantum optimal transport and applications
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DOI：
10.1007/s11128-019-2519-8
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发表时间：
2020-01-01
影响因子：
2.5
通讯作者：
Ikeda, Kazuki
中科院分区：
文献类型：
--
作者：
Ikeda, Kazuki
量子最优输运寻求在输运过程中必须满足的约束条件下，将一个量子态输运到另一个量子态的总成本最小化的算子。本文将经典的最优运输理论Monge-Kantorovich问题进行推广，并给出了一些应用。作为一个例子，我们解决了无限重复的量子博弈，并建立了量子囚徒困境的民间定理，该定理声称相互合作可以是无限重复量子博弈的一种均衡。我们还列举了一系列的例子来说明抽象量子最优输运理论的通用性和实用性。
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.