The Infinitesimal Structure of Quantum Information
Quantum Physics
2026-07-14 v1 Mathematical Physics
Algebraic Geometry
Differential Geometry
Quantum Algebra
Abstract
This paper establishes a rigorous, unified geometric framework for quantum state spaces by constructing smooth, regular embeddings into higher-order dual number algebras , wherein every quantum state is faithfully represented as a non-reduced scheme-theoretic point. We show that under this unified family of truncated rings, the non-linear matrix commutators governing the Liouville-von Neumann dynamics map globally onto flat, linear, and rigid algebraic flows, establishing nilpotent dual algebras as a pristine geometric landscape for higher-dimensional quantum kinematics.
Keywords
Cite
@article{arxiv.2607.12559,
title = {The Infinitesimal Structure of Quantum Information},
author = {Luca Barbieri-Viale},
journal= {arXiv preprint arXiv:2607.12559},
year = {2026}
}