---
title: "GHZ 关联：四种设置，拼不出的局域指令表"
description: "理想情况下确定无疑的矛盾，为何仍要认真记录不完美探测？"
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page_type: "story"
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  en: "https://sandboxphysics.com/stories/quantum-evidence/ghz-parity-three-photon-records/"
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

# GHZ 关联：四种设置，拼不出的局域指令表

Sandbox Physics · 2026-10-18

理想情况下确定无疑的矛盾，为何仍要认真记录不完美探测？

## 三个纠缠光子，四个已探测光子

Bouwmeester 等人的 1999 年实验组合两对光子，同时筛选一个触发探测与另外三臂的探测。因此，三光子 GHZ 证据以四重符合为条件。单独一次触发点击，并不能认证一组三光子已经作为可独立使用的资源送达。

论文检验目标偏振分量，以及分量之间的相干性。这是不同问题：非相干混合也能重现分量布居。Pan 等人的 2000 年实验进一步用四种偏振设置检验 GHZ 非局域性论证。制备状态与检验一组特定关联矛盾，是相关但记录要求不同的成果。

证据阅读：D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter and A. Zeilinger (1999), Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement, PRL 82, 1345–1349 J.-W. Pan et al. (2000), Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403, 515–519 — abstract and figure captions

## 先约定相位，再相乘符号

在自己的计算中，每臂以零表示水平偏振、一表示竖直偏振，取全零与全一分量等幅、正号的叠加。第一种分析器称为 X，区分两种对角线偏振；第二种称为 Y，区分等幅但相对虚相位相反的叠加，其正结果的竖直分量具有正虚振幅。

这样无需借助容易混淆的圆偏振左右旋名称，就明确了结果符号。1999 年论文写出的两个分量将第三个偏振反转，对该臂作局域比特翻转即可转成这里的约定。改变态相位或重标分析器结果，都会改变相关奇偶符号，必须配套处理。

$$
\begin{gathered}|G_+\rangle=\frac{|000\rangle+|111\rangle}{\sqrt{2}},\\ \langle XXX\rangle=1,\quad\langle XYY\rangle=-1,\\ \langle YXY\rangle=\langle YYX\rangle=-1\end{gathered}
$$

证据阅读：D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter and A. Zeilinger (1999), Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement, PRL 82, 1345–1349 D. M. Greenberger, M. A. Horne and A. Zeilinger (1989), Going Beyond Bell’s Theorem — original contribution made available as arXiv:0712.0921 in 2007

## 矛盾出在一张共同的指令表

假设某种局域确定性描述，为每站的两种分析器选择都预先指定答案，而且不依赖远方的选择。一共六个二值答案，所以完整指令表共有 64 张。在此约定下，每种含两个 Y 选择的测量情境，都要求三站结果乘积为负。

把这三个要求相乘，每个预定 Y 答案出现两次，剩下三个 X 答案的乘积为负，量子理论却预言为正。穷举发现八张表满足前三个要求，但全部不满足第四个。没有一张表同时满足四项；把指令表随机混合，也无法得到四个完美关联。

证据阅读：D. M. Greenberger, M. A. Horne and A. Zeilinger (1989), Going Beyond Bell’s Theorem — original contribution made available as arXiv:0712.0921 in 2007 J.-W. Pan et al. (2000), Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403, 515–519 — abstract and figure captions

## 相容的乘积，不等于局域答案能同时测量

每个测量情境在三个分离光子上各选一个分析器，所以能相乘这三个结果；四个整体乘积算符也彼此对易。然而，同一光子上的 X 与 Y 并不因此变得可以同时测量。不同情境用的是反复制备系综中的不同成员。

独立计算对每个情境的八种结果逐项求和复振幅，得到四种允许结果各有四分之一概率，错误奇偶性的概率为零。各站单独的结果仍然均衡。确定的是乘积，而非可在本地预知的单光子结果，更不是能操纵的远程消息。

证据阅读：D. M. Greenberger, M. A. Horne and A. Zeilinger (1989), Going Beyond Bell’s Theorem — original contribution made available as arXiv:0712.0921 in 2007

## 有限计数替代理想保证

真实记录包括错误奇偶性、漂移与不确定度。自己的穷举还表明，若四种情境均匀选择，局域指令最多平均满足其中三种。等价地，带符号关联和的上界为二，而这里的理想量子态给出四。这是独立有限得分计算，不是对历史数据的拟合。

在明确声明的白噪声教学模型中，理想 GHZ 态占百分之六十时，各目标奇偶性成功率为百分之八十，关联和为 2.4。这个数字本身没有给出实验显著性。试次定义、设置独立性、停止规则与实际各结果计数，才能决定适用的统计检验。

证据阅读：D. M. Greenberger, M. A. Horne and A. Zeilinger (1989), Going Beyond Bell’s Theorem — original contribution made available as arXiv:0712.0921 in 2007 J.-W. Pan et al. (2000), Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403, 515–519 — abstract and figure captions

## 漏掉的事件仍然限制结论

四重符合只保留光源尝试中很小的已探测子集。要对这份筛选记录套用同一个局域模型界限，需要公平采样等抽样假设，或明确计入未探测的试次设计。触发信号本身不会关闭探测漏洞，局域性还需要另行核对时空关系与设置选择。

所选奇偶关联也没有重建三比特密度矩阵的每个元素。链接的双光子 Bell 与单比特层析 Lab 分别说明其他问题，均未复现这套装置。这里的成果是在声明的采集假设下检验多粒子关联，不是无条件光源、完整态表征或完全无漏洞实验。

证据阅读：D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter and A. Zeilinger (1999), Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement, PRL 82, 1345–1349 J.-W. Pan et al. (2000), Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403, 515–519 — abstract and figure captions

## 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。

- [比较另一种双光子 Bell 得分](https://sandboxphysics.com/zh/labs/bell-chsh/)
- [区分奇偶检验与态重建](https://sandboxphysics.com/zh/labs/quantum-state-process-tomography/)

## 来源与阅读说明

本文核读五页 1999 年 PRL，以及以 arXiv:0712.0921 提供的 GHZ 原始论述。2000 年 Nature 实验仅访问到出版方摘要与图注，全文受订阅限制。下文正相位三比特约定、局域指令穷举与复振幅检验均为独立教学计算，并未重建历史计数。

1. [D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter and A. Zeilinger (1999), Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement, PRL 82, 1345–1349](https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.82.1345)
2. [J.-W. Pan et al. (2000), Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403, 515–519 — abstract and figure captions](https://www.nature.com/articles/35000514)
3. [D. M. Greenberger, M. A. Horne and A. Zeilinger (1989), Going Beyond Bell’s Theorem — original contribution made available as arXiv:0712.0921 in 2007](https://arxiv.org/pdf/0712.0921)

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