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
本研究通过条件记录准则和四个模型，证明孤立概率的无信号约束不足以保证重复读出或组合下的记录一致性，并给出泄漏界限、修正矩阵及有限资源障碍等条件。
AI 中文摘要
对孤立结果概率的无信号约束并不能决定装置在重复读出、网络组合或重用下是否保持其可访问记录的联合分布。我们通过条件记录准则和四个显式模型研究这些扩展。对于包裹柯西溯因源，在两个条件独立的连续读出下进行保护要求角度无关的响应；在无连续性假设下，三次读出即可满足。有限角带宽假设给出定量泄漏界限，而仅连续性不提供均匀稳定性。在指定的双源贝尔节点，所需修正矩阵在每个偶数均匀角网格上具有完全非负秩。高斯控制器可以消除分支质量依赖性，同时留下可区分的联合记录，我们为此推导出精确的噪声和法律变化权衡。最后，具有共享经典噪声的固定单重态再现了可变宽度孤立结果族，但保留和刷新的控制器产生不同的时间统计。我们证明了有限资源障碍并构造了正有限控制器近似。包含830万次独立模拟历史的数值研究支持特定模型的预测。总之，这些结果确定了在将装置扩展到更丰富的记录和干预时，必须伴随边际无信号的条件。
英文摘要
No-signalling constraints on isolated outcome probabilities do not determine whether an apparatus preserves the joint law of its accessible records under repeated readout, network composition, or reuse. We study these extensions through a conditional-record criterion and four explicit models. For a wrapped-Cauchy retrocausal source, protection under two conditionally independent continuous readouts forces an angle-independent response; three readouts suffice without continuity. A finite angular-bandwidth assumption gives a quantitative leakage bound, whereas continuity alone gives no uniform stability. At a specified two-source Bell junction, the required correction matrix has full nonnegative rank on every even uniform angular grid. A Gaussian controller can cancel branch-mass dependence while leaving a distinguishable joint record, for which we derive exact noise and law-change tradeoffs. Finally, a fixed singlet with shared classical noise reproduces the variable-width isolated outcome family, but retained and refreshed controllers generate different temporal statistics. We prove a finite-resource obstruction and construct positive finite-controller approximations. Numerical studies comprising 8.3 million independent simulated histories support the model-specific predictions. Together, the results identify conditions that must accompany marginal no-signalling when extending an apparatus to richer records and interventions.
