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L. Barbieri-Viale

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Preprint Aug 2026

Quantum Information at Infinity

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...

L. Barbieri-Viale · 0 citations

Preprint Jul 2026

The Infinitesimal Structure of Quantum Information

This paper establishes a rigorous, unified geometric framework for quantum state spaces by constructing smooth, regular embeddings into higher-order dual number algebras $\mathcal{Q}_N \equiv \mathbb{R}[\varepsilon]/(\varepsilon^{N^2-1})$, wherein every quantum state is faithfully represented as a non-reduced scheme-th...

L. Barbieri-Viale · 0 citations