无穷远处的量子信息
Quantum Information at Infinity
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中文总结 AI 辅助
该研究引入无穷远处量子信息空间Quinfinity，将纯态预簇等化为经典Fisher-Rao统计流形，推导得出开放Gorini-Kossakowski-Sudarshan-Lindblad渐近主方程，揭示海森堡不确定性原理的无穷远正则化机制。
中文摘要 AI 辅助
我们引入无穷远处量子信息空间（Quinfinity）$\boldsymbol{\textit{Q}}_\boldsymbol{\textit{\textbackslash{}infty}}$，将其作为符号量子N空间$\boldsymbol{\textit{Q}}_\boldsymbol{\textit{\textit{N}}}$的逆极限，等同于进拓扑下的形式幂级数完备局部实代数。纯态预簇被形式化为N能级纯态簇的逆极限，由实根式理想直系统的代数余极限驱动。这一实结构内化了虚数单位，将度量几何坍缩为不变黎曼等距变换，直接将预簇等同于经典Fisher-Rao统计流形。在该框架内，海森堡不确定性原理在无穷远处经历结构正则化，本质上表现为由进代数导数支配的局域截断障碍。同时，连续Liouville-von Neumann方程作为预簇的内部切导数运算，而开放的Gorini-Kossakowski-Sudarshan-Lindblad渐近主方程通过非结合对称Jordan积被本质上推导得出。该耗散流作为收缩径向向量场，抑制高阶射流构型，驱动状态轨迹沿层级树向下趋向绝对零元，该零元为非奇异通用吸引子。
英文摘要
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.
