AI 中文总结
该研究明确四元数与八元数量子模型的运算基础，刻画四元数信道的精确条件与纠错特性，对比各类非结合性量子模型的结构差异，揭示精确环境表示不会抹去物理理论的核心结构。
AI 中文摘要
标量场本身无法确定一个量子理论：态、效应、过程、对称性、复合与丢弃同样是其结构组成部分。实化（Realification）阐明了这一点：正交复结构J²=-I选取物理实算子与平衡复合结构。四元数量子力学在由反酉辛结构Θ²=-I选取的加倍复空间上有类似的精确表示。在该扇区内，Choi不动点条件刻画了复信道何时允许四元数Kraus算子，而有限维右四元数量子码的精确纠错由实中心中的压缩系数刻画，并允许显式恢复。对于八元数，非结合性排除了唯一延续；仿线性、范畴、扇区、Jordan、Clifford包络与Moufang模型，按其保留的运算结构及定义复合、信道或恢复所需的额外数据进行比较。在所有这些情形中，精确的环境表示不会抹去选取物理理论的复或辛结构。
英文摘要
A scalar field alone does not determine a quantum theory: states, effects, processes, symmetries, composition, and discard are equally structural. Realification illustrates this point: an orthogonal complex structure J^2 = -I selects the physical real operators and the balanced composite. Quaternionic quantum mechanics has an analogous exact representation on a doubled complex space selected by an antiunitary symplectic structure Theta^2 = -I. Within that sector, a Choi fixed-point condition characterizes when a complex channel admits quaternionic Kraus operators, while exact correction of a finite-dimensional right-quaternionic code is characterized by compression coefficients in the real center and admits an explicit recovery. For octonions, nonassociativity precludes a unique continuation; para-linear, categorical, sectorial, Jordan, Clifford-envelope, and Moufang models are compared by the operational structures they retain and the additional data required to define composites, channels, or recovery. Across these cases, an exact ambient representation does not erase the complex or symplectic structure that selects the physical theory.
Comments25 pages; no figures
