Scattering Measures and Information Geometry
Abstract
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.
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BibTeX
@misc{oda2026scattering,
title = {{Scattering Measures and Information Geometry}},
author = {Tatsuro Oda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34721},
eprint = {2609.34721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scattering Measures and Information Geometry
AU - Tatsuro Oda
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34721
UR - https://arxiv.org/abs/2609.34721
AB - 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.
ER -