Quantum Information at Infinity
Abstract
We introduce the Quantum Information Space at Infinity (Quinfinity) π¬β as the inverse limit of the symbolic Quantum N-Spaces π¬N, identified with the complete local real algebra of formal power series under the adic topology. The pure state pro-variety is formalized as the inverse limit of N-level pure state varieties, driven by the algebraic colimit of a direct system of real radical ideals. This real architecture internalizes the imaginary unit, collapsing the metric landscapes onto an invariant Riemannian isometry, which identifies the pro-variety directly with the classical Fisher-Rao statistical manifold. Within this framework, the Heisenberg uncertainty principle undergoes a structural regularization at infinity being intrinsically manifested as a localized truncation obstruction governed by adic algebraic derivations. Concurrently, the continuous Liouville-von Neumann equation operates as an internal derivation tangent to the pro-variety, while the open Gorini-Kossakowski-Sudarshan-Lindblad asymptotic master equation is intrinsically obtained via a non-associative symmetric Jordan product. This dissipative flow acts as a contracting radial vector field that dampens higher-order jet configurations, driving the state trajectories down the hierarchical tree toward the absolute zero element as a non-singular universal attractor.
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BibTeX
@misc{barbieriviale2026quantum,
title = {{Quantum Information at Infinity}},
author = {L. Barbieri-Viale},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27498},
eprint = {2608.27498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27498},
}
RIS
TY - UNPB
TI - Quantum Information at Infinity
AU - L. Barbieri-Viale
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27498
UR - https://arxiv.org/abs/2608.27498
AB - We introduce the Quantum Information Space at Infinity (Quinfinity) π¬_β as the inverse limit of the symbolic Quantum N-Spaces π¬_N, identified with the complete local real algebra of formal power series under the adic topology. The pure state pro-variety is formalized as the inverse limit of N-level pure state varieties, driven by the algebraic colimit of a direct system of real radical ideals. This real architecture internalizes the imaginary unit, collapsing the metric landscapes onto an invariant Riemannian isometry, which identifies the pro-variety directly with the classical Fisher-Rao statistical manifold. Within this framework, the Heisenberg uncertainty principle undergoes a structural regularization at infinity being intrinsically manifested as a localized truncation obstruction governed by adic algebraic derivations. Concurrently, the continuous Liouville-von Neumann equation operates as an internal derivation tangent to the pro-variety, while the open Gorini-Kossakowski-Sudarshan-Lindblad asymptotic master equation is intrinsically obtained via a non-associative symmetric Jordan product. This dissipative flow acts as a contracting radial vector field that dampens higher-order jet configurations, driving the state trajectories down the hierarchical tree toward the absolute zero element as a non-singular universal attractor.
ER -