Quantum Information at Infinity

• URL: http://arxiv.org/abs/2608.27498v1
• Date: Thu, 27 Aug 2026 02:12:05 GMT
• Title: Quantum Information at Infinity
• Abstract summary: We introduce the Quantum Information Space at Infinity (Quinfinity) $mathcalQ_infty$ as the inverse limit of the symbolic Quantum $N$-Spaces $mathcalQ_N$.<n>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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Quantum Information Space at Infinity (Quinfinity) $\mathcal{Q}_\infty$ as the inverse limit of the symbolic Quantum $N$-Spaces $\mathcal{Q}_N$, 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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