发表机构
Monash University（莫纳什大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在逆因果模型中区分两种复合要求，通过不变空间和观测空间刻画隐变量模型的记录保持与不可区分性，并给出有限状态反例及连续源下的定量结果。
AI 中文摘要
一个隐变量模型可以重现与上下文无关的单个读数，但在设备连接或重复使用时却无法保持可观测记录。我们区分两种复合要求。对于有限族的非负仪器矩阵，由归一化缺陷生成的不变空间刻画了在每种有限自适应策略下的单位延续质量。其零化子定义了在结果条件更新下封闭的最大容许正锥。一个单独的观测空间刻画了在联合读数下上下文相关隐藏制备的不可区分性。一个有限状态示例通过了每个固定序列但在依赖结果的停止下失败。对于具有明确规定的未改变源被动扩展的包裹柯西自旋源，两个单独公平的探针获得设置相关的同意概率，对比度为ε²sech(2g)/4。更一般地，在一次和两次相同使用下的保护迫使连续二元被动响应为常数；可测量的二值例外仍然可能。精确有理计算、穷举有限策略实验、连续源采样和求积法检验了所述示例。这些准则适用于指定的仪器族和可访问记录；它们不构建微观探测器或建立无限制网络复合下的一致性。
英文摘要
A hidden-variable model can reproduce context-independent individual readouts while failing to preserve observable records when devices are connected or reused. We distinguish two composition requirements. For a finite family of nonnegative instrument matrices, an invariant space generated by normalization defects characterizes unit continuation mass under every finite adaptive policy. Its annihilator defines the maximal admissible positive cone closed under outcome-conditioned updates. A separate observation space characterizes indistinguishability of context-dependent hidden preparations under joint readout. A finite-state example passes every fixed sequence but fails under outcome-dependent stopping. For a wrapped-Cauchy spin source with an explicitly stipulated unchanged-source passive extension, two individually fair probes acquire a setting-dependent agreement probability with contrast $ε^2\operatorname{sech}(2g)/4$. More generally, protection under one and two identical uses forces a continuous binary passive response to be constant; measurable two-valued exceptions remain possible. Exact rational calculations, exhaustive finite-policy experiments, continuous source sampling, and quadrature test the stated examples. The criteria apply to specified instrument families and accessible records; they do not construct a microscopic detector or establish consistency under unrestricted network composition.
