Conservative Motion Theory – Information IV Fredholm Quantum Information and the Entanglement Metric

Kawasaki, Hideyo

Published Nov 19, 2025• 0 citations

Abstract

We develop a fully operator-theoretic formulation of quantum information within theframework of Conservative Motion Theory (CMT). Given a family of density matricesρθ, we introduce a reflection–positive Fredholm kernel whose κ → 0+ spectral responsereproduces the quantum Fisher information (QFI), the Bures metric, and measures ofquantum entanglement. Entanglement negativity, quantum mutual information, and thequantum geometry tensor all arise as Fredholm spectral invariants. This establishes a unifiedanalytic framework for quantum information.

DOI: 10.5281/zenodo.17648150

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