希尔伯特空间概率的操作阴影
Operational Shadows of Hilbert-Space Probabilities
AI总结：
研究在量子情境中，通过校准旋钮改变测量配置时概率的变化，对比不同响应模型，探讨操作重合与多情境非经典性，借助法卡斯引理明确经典扩展存在与否的条件。
AI中文摘要：
在一个固定设置下，在精确量子情境中观察到的概率，作为探测器点击统计，与经典划分原子上的普通概率无法区分。但实际分析仪通常有一个校准旋钮。若通过该物理参数连续改变测量配置，操作对象不再是单纯形的一个点而是一条响应曲线。经典线性响应、马吕斯型希尔伯特空间响应、softmax链接、非同态参数转录和不连续阈值限制是从设置到概率的不同映射。连续性、校准和物理合成定律的保持是旋钮实验意义的一部分。这种比较区分了特定的、校准的响应模型；它们本身并不构成经典与量子的不可能定理。静态操作重合在两个交织情境中也可能持续：若共同结果有相同概率，其余质量总能通过经典联合分布耦合。当一族局部阴影不能粘合成一个非负全局分布或一个单纯形分解时，真正 的多情境非经典性开始。法卡斯引理给出了确切的选择：要么存在经典扩展，要么一个分离线性不等式证明其不可能。
英文摘要：
At one frozen setting, the probabilities observed in a sharp quantum context are indistinguishable, as detector-click statistics, from ordinary probabilities on the atoms of a classical partition. But an actual analyzer usually comes with a calibrated knob: a tangible handle on the apparatus. If the measurement configuration is co-varied continuously through this physical parameter, the operational object is no longer one point of a simplex but a response curve. Classical linear responses, Malus-type Hilbert-space responses, softmax links, non-homomorphic parameter transcriptions, and discontinuous threshold limits are different maps from settings to probabilities. Continuity, calibration, and preservation of the physical composition law are then part of the experimental meaning of the knob. Such comparisons distinguish specified, calibrated response models; by themselves they do not constitute a classical-versus-quantum impossibility theorem. The static operational coincidence can also persist for two intertwined contexts: if the common outcomes receive the same probabilities, the remaining masses can always be coupled by a classical joint distribution. Genuine multi-context nonclassicality begins when a family of local shadows cannot be glued into one nonnegative global distribution or one simplex factorization. Farkas' lemma gives the exact alternative: either the classical extension exists, or a separating linear inequality certifies its impossibility.
