We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel’s smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel’s smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes, which significantly simplifies the study of channel simulation and provides insights and bounds for the case under entanglement-assisted codes. Third, we derive the asymptotic equipartition property of the channel’s smooth max-information; i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.

中文翻译：

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量子通道模拟和通道的平滑最大信息

我们研究了量子信道模拟的一般框架，即一个量子信道使用不同类别的代码模拟另一个信道的能力。首先，我们证明了在无信号辅助码下模拟的最小误差和一次性量子模拟成本是由半定程序给出的。其次，我们引入了通道的平滑最大信息，它可以看作是对量子通道互信息的一次性推广。我们提供了信道平滑最大信息的精确操作解释，作为无信令辅助码下的一次性量子模拟成本，这显着简化了信道模拟的研究，并为纠缠辅助码下的情况提供了见解和界限。第三，我们推导出通道平滑最大信息的渐近均分特性；即在独立同分布渐近极限收敛到信道的量子互信息。这意味着存在无信号相关的量子逆香农定理。最后，我们探讨了各种量子通道的模拟成本。