发表机构
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文以Fisher度量定义散射测度的信息几何，将散射实验纳入信息论框架，并连接最优实验设计，同时阐明其在量子测量层级中的位置。
AI 中文摘要
我们将散射实验表述为结果空间上的参数化有限测度，并发展了由Fisher度量定义的相应信息几何。将散射测度分解为总质量和归一化形状，可将Fisher信息分解为整体散射强度变化和结果间重新分布两部分的贡献。测量过程由作用于散射测度上的概率或亚概率核表示。此类核收缩Fisher信息，将一大类实验操作纳入共同的信息论框架。这一表述通过散射测度的Fisher几何将散射实验与最优实验设计理论联系起来。相同的有限测度结构在具有不完全探测的量子测量中自然出现，阐明了其在从量子测量到经典结果统计的层级中的位置。
英文摘要
We formulate scattering experiments in terms of parameterized finite measures on outcome spaces and develop the associated information geometry defined by the Fisher metric. The decomposition of a scattering measure into total mass and normalized shape separates Fisher information into contributions from changes in overall scattering strength and redistribution among outcomes. Measurement processes are represented by probability or sub-probability kernels acting on the scattering measure. Such kernels contract Fisher information, placing a broad class of experimental operations within a common information-theoretic framework. This formulation connects scattering experiments to the theory of optimal experimental design through the Fisher geometry of scattering measures. The same finite-measure structure arises naturally in quantum measurements with incomplete detection, clarifying its place in the hierarchy from quantum measurement to classical outcome statistics.
Comments47 pages, 7 figures
