We study one-mode Gaussian quantum channels in continuous-variable systems by performing a black-box characterization using complete positivity and trace preserving conditions, and report the existence of two subsets that do not have a functional Gaussian form. Our study covers as a particular limit the case of singular channels, thus connecting our results with their known classification scheme based on canonical forms. Our full characterization of Gaussian channels without Gaussian functional form is completed by showing how Gaussian states are transformed under these operations, and by deriving the conditions for the existence of master equations for the non-singular cases. We show that although every functional form can be found in the vicinity of the identity, one of them does not parametrize unitary channels.

中文翻译：

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高斯函数形式以外的单模高斯通道的位置表示

我们通过使用完全正性和迹线保留条件执行黑盒表征来研究连续变量系统中的单模高斯量子通道，并报告存在两个不具有功能性高斯形式的子集。我们的研究特别涵盖了奇异通道的情况，因此将我们的结果与基于规范形式的已知分类方案联系起来。通过显示高斯状态如何在这些操作下进行转换，以及推导非奇异情况下主方程存在的条件，可以完成对没有高斯函数形式的高斯通道的完整表征。我们显示，尽管可以在标识附近找到每种功能形式，但其中一种不会参数化单一通道。