We set up a general theory leading to a quantum Wasserstein distance of order 1 between channels in an operator algebraic framework. This gives a metric on the set of channels from one composite system to another, which is deeply connected to reductions of the channels. The additivity and stability properties of this metric are studied.

中文翻译：

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通道间 1 阶量子 Wasserstein 距离

我们建立了一个通用理论，导致算子代数框架中通道之间的量子 Wasserstein 距离为 1 阶。这给出了从一个复合系统到另一个复合系统的通道集的度量，这与通道的减少密切相关。研究了该度量的可加性和稳定性。