CHSH实验中定域实在论的精确代价：测量依赖-探测权衡曲面、使其饱和的莫尔相位锁定机制，以及四重符合求和中的未测量条纹
The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum
中文总结 AI 辅助
本文推导了CHSH实验中定域实在论的测量依赖-探测权衡曲面，提出可饱和该曲面的莫尔相位锁定机制，发现四重符合求和中存在未测量条纹，为定域实在论的边界提供了精确约束。
中文摘要 AI 辅助
针对CHSH实验中忠实的定域隐变量解释——其需重现观测到的单计数率与符合计数率，以及具有对称探测器效率η_eff的偏振单态的无偏边缘分布——本文确定了实现CHSH值S所需的最小测量依赖度M（Hall的变分度量）。对所有定域策略进行线性规划，在32个网格点上达到机器精度，得到M(S,η_eff)=max{0,η_eff((S+2)η_eff−4)/6}，其边界在η_eff=1时重现Hall的紧约束、Garg-Mermin探测阈值，以及后选择上限S=4/η_eff−2。量子点被精确验证：M(2√2,9/10)=(27√2−33)/100，其原始与对偶证书在Q(√2)算术域中。本文求解了唯一的探测轮廓D(m)=√m h(m)，在该轮廓下确定性符号模型可精确重现单态；推导了√m边界定律，并证明对于此类纯探测模型，精确量子关联与角度无关的符合计数率无法同时成立。存活的定域解释在测量依赖度与四重符合求和的cos4(a−b)调制间存在权衡，该调制相对振幅最高达12.4%，在CHSH角处完全消失，且似乎从未被限制在1%以下。设置环协议可在数小时内达到0.1%水平的5σ灵敏度：平坦结果将迫使M≥Hall下限的95%；条纹则会与量子力学的平坦率预测矛盾。最后，本文提出一种定域机制——莫尔相位锁定，其具有确定性相位演化，所有随机性在冻结的晶格偏移与飞行时间中被淬灭，该机制在η_eff=1（均匀保真度为10%）时精确达到已验证的下限；其对关联极值的软化是可证伪的指纹。
英文摘要
For local hidden-variable accounts of the CHSH experiment that are faithful -- reproducing the observed singles and coincidence rates and unbiased marginals of a polarization singlet with symmetric detector efficiency $η_{\rm eff}$ -- I determine the minimal measurement dependence $M$ (Hall's variational measure) needed to achieve a CHSH value $S$. Linear programming over all local strategies yields, to machine precision at 32 grid points, $M(S,η_{\rm eff})=\max\{0,η_{\rm eff}((S+2)η_{\rm eff}-4)/6\}$, whose edges reproduce Hall's tight bound at $η_{\rm eff}=1$, the Garg-Mermin detection threshold, and the postselection ceiling $S=4/η_{\rm eff}-2$. The quantum point is certified exactly: $M(2\sqrt{2},9/10)=(27\sqrt{2}-33)/100$, with primal and dual certificates in $\mathbb{Q}(\sqrt{2})$ arithmetic. I solve the unique detection profile $D(m)=\sqrt{m}\,h(m)$ under which a deterministic sign model reproduces the singlet exactly, derive the $\sqrt{m}$ edge law, and prove exact quantum correlations and angle-independent coincidence rates jointly impossible for pure-detection models. Surviving local accounts trade off measurement dependence against a $\cos 4(a-b)$ modulation of the fourfold coincidence sum, of relative amplitude up to 12.4%, which vanishes at the CHSH angles and has never been bounded below 1%. A settings-torus protocol reaches $5σ$ sensitivity at 0.1% within hours: a flat result forces $M\gtrsim 95\%$ of Hall's floor; a fringe would contradict the flat-rate prediction of quantum mechanics. Finally I exhibit a local mechanism -- moire phase locking -- with deterministic phase evolution and all randomness quenched in frozen offsets and flight times; with 1024 offsets it attains the certified floor exactly at $η_{\rm eff}=1$ at every tested register fidelity, from 10% to 1%, and its softening of the correlation extremes is a falsifiable fingerprint.
