--- title: "光子 Bell 检验：没有点击的试次也要入账" description: "高效探测器、另一份事件账本与局域时钟，怎样把分别取得的漏洞进展放进同一次实验？" canonical_url: "https://sandboxphysics.com/zh/stories/quantum-evidence/photon-bell-losses-optical-trials/" language: "zh-CN" page_type: "story" alternate_languages: en: "https://sandboxphysics.com/stories/quantum-evidence/photon-bell-losses-optical-trials/" last_modified: "2026-10-18" --- [量子物理：读懂证据](https://sandboxphysics.com/zh/stories/quantum-evidence/) 诺奖 A · 证据与操控 # 光子 Bell 检验：没有点击的试次也要入账 Sandbox Physics · 2026-10-18 高效探测器、另一份事件账本与局域时钟，怎样把分别取得的漏洞进展放进同一次实验？ ## 高效探测器改变了问题 2013 年，Giustina 等人违反光子 Bell 不等式，无需假定已探测光子对能公平代表每个发射光子对。超导转变边缘传感器与高效收集，把损失降到适合 Eberhard 检验的程度。这项进展处理探测问题，并未同时确立后来实验那样快速、类空间分隔的设置选择。 未探测光子不是可以删掉的一行缺失数据。只保留符合，会允许探测依赖隐含指令及设置；即使留下的光子对给出漂亮偏振曲线，局域解释仍可能存在。更好探测之所以重要，是因为不等式要为不成功事件记账。 证据阅读：M. Giustina et al. (2013), Bell violation using entangled photons without the fair-sampling assumption, Nature 497, 227–230 — author manuscript ## 每次光学试次都写一个结果 下式约定中，加号表示指定通道出现点击，零表示该通道没有点击。每个概率都以编号标出的局域设置为条件。2015 年两个团队都使用这种 Clauser–Horne–Eberhard 形式：有利的双点击必须超过三个明确定义的惩罚项，其中包括单侧未探测。 无需量子理论就能核对局域界限。预先为两侧的每种设置各指定点击或不点击，穷举十六种指令，得到八个零分、八个负一分；随机混合不能变成正值。双侧无点击的试次贡献零分，却仍留在概率分母里。 $$ \begin{aligned}J={}&p_{++}(1,1)-p_{+0}(1,2)\\ &-p_{0+}(2,1)-p_{++}(2,2)\\ J_{\mathrm{local}}&\leq0\end{aligned} $$ 证据阅读：M. Giustina et al. (2015), Significant-loophole-free test of Bell’s theorem with entangled photons, PRL 115, 250401 — author manuscript L. K. Shalm et al. (2015), Strong Loophole-Free Test of Local Realism, PRL 115, 250402 — author manuscript, revised 2016 ## 少一点纠缠可以换来更多证据 把理想关联做到最大，与在损失下把违反做到最大，并不是同一任务。Eberhard 类优化采用不相等的偏振对振幅及配套角度，压低代价高的事件。理想对称、无背景极限下，效率门槛趋近三分之二；真实背景及不完美状态会抬高要求。 这里的效率把透射、收集与探测一起计算，不能仅凭探测器规格认证整套实验。调节状态也不等于可以减去不方便的单点击。态制备与分析角度必须改善完整事件账本；两个 2015 年装置各自使用优化状态及自身效率。 证据阅读：P. H. Eberhard (1993), Background level and counter efficiencies required for a loophole-free Einstein-Podolsky-Rosen experiment — APS abstract M. Giustina et al. (2013), Bell violation using entangled photons without the fair-sampling assumption, Nature 497, 227–230 — author manuscript L. K. Shalm et al. (2015), Strong Loophole-Free Test of Local Realism, PRL 115, 250402 — author manuscript, revised 2016 ## 先由脉冲定义试次，再谈符合 维也纳实验把源脉冲与快速设置变化同步到一兆赫时钟，结果落在局域定义的时间槽中。Shalm 团队则使用每秒约九万九千次的同步信号，在一次开关区间内容纳数个可能的泵浦脉冲槽。这是不同光学时序，试次数不能互换。 在 Shalm 团队的几何中，有些时间槽不满足时空约束，报告的聚合采用合适的中央槽。加入额外脉冲可以增加计数，也可能破坏分隔。每侧设置选择必须位于相关发射光锥之外，且来不及影响远端结果，并计入实测延迟及不确定度。 证据阅读：M. Giustina et al. (2015), Significant-loophole-free test of Bell’s theorem with entangled photons, PRL 115, 250401 — author manuscript L. K. Shalm et al. (2015), Strong Loophole-Free Test of Local Realism, PRL 115, 250402 — author manuscript, revised 2016 ## 把每个团队的统计陈述留在原处 维也纳报告的 p 值上界为三点七四乘以十的负三十一次方，允许器件记忆，并计入量化的额外设置可预测性。Shalm 团队的五脉冲分析报告约五点八乘以十的负九次方；采用保守可预测性余量后，上界变为二点三乘以十的负七次方。 这些数值属于各自的记录及分析，不能拼成一次虚构实验。p 值约束的是在局域零假设及其输入假设下，统计量达到指定极端程度的机会；它不是局域性为真的概率。极小统计上界也没有衡量全部标定或人为错误。 证据阅读：M. Giustina et al. (2015), Significant-loophole-free test of Bell’s theorem with entangled photons, PRL 115, 250401 — author manuscript L. K. Shalm et al. (2015), Strong Loophole-Free Test of Local Realism, PRL 115, 250402 — author manuscript, revised 2016 ## 把保留的假设写出来 局域时序规则阻止符合搜索器利用远隔两端的探测时间选择光子对。新鲜设置与有根据的可预测性上界依旧重要。时空位置约束特定因果联系，却不能用实验排除延伸到共同过去的任意关联；结果何时完成，也需要明确物理约定。 链接的 Bell Lab 演示关联与采样选择，没有实现任何一方的光子源、脉冲槽记录、超导探测器或有限样本检验。本文枚举检查的是不等式的事件逻辑，不是历史时序测绘或报告显著性。证据挑战指定局域模型，并不提供可控超光速信号。 证据阅读：M. Giustina et al. (2015), Significant-loophole-free test of Bell’s theorem with entangled photons, PRL 115, 250401 — author manuscript L. K. Shalm et al. (2015), Strong Loophole-Free Test of Local Realism, PRL 115, 250402 — author manuscript, revised 2016 ## 接着操作模型 以下为已有教学 Lab；其模拟记录与上文历史观测分别对待。 - [检查教学模型的采样假设](https://sandboxphysics.com/zh/labs/bell-chsh/) ## 来源与阅读说明 本文通过 arXiv 核读 Giustina 2013 年及两个团队 2015 年的光子原稿，重点检查不等式、试次定义与时序及统计讨论。Eberhard 1993 年 APS 摘要可读，全文未能获取。确定性枚举是本文说明性核对，不是实验记录再分析。 1. [M. Giustina et al. (2013), Bell violation using entangled photons without the fair-sampling assumption, Nature 497, 227–230 — author manuscript](https://arxiv.org/pdf/1212.0533) 2. [M. Giustina et al. (2015), Significant-loophole-free test of Bell’s theorem with entangled photons, PRL 115, 250401 — author manuscript](https://arxiv.org/pdf/1511.03190) 3. [L. K. Shalm et al. (2015), Strong Loophole-Free Test of Local Realism, PRL 115, 250402 — author manuscript, revised 2016](https://arxiv.org/pdf/1511.03189) 4. [P. H. 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