By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators.

中文翻译：

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泊松量子信息

通过对一系列稀有量子物体取泊松极限，我推导出了 Uhlmann 保真度、量子 Chernoff 量、相对熵和 Helstrom 信息的简单公式。我还介绍了经典信息论中泊松模型的类似公式。称为强度算子的算子作为描述泊松状态的形式主义中的中心量出现。它的行为类似于密度算子，但未归一化。强度算子方面的公式不仅类似于密度算子方面的一般公式，而且与一些现有的非归一化正半定矩阵之间的散度定义相吻合。此外，我表明某些通道对泊松态的影响可以通过强度算子的简单映射来描述。