[论文解读] Bounding quantum theory with the exclusivity principle in a two-city experiment

Mohamed Nawareg, F. Bisesto+5 more|arXiv (Cornell University)|Nov 14, 2013

Quantum Mechanics and Applications参考文献 39被引用 7

一句话总结

本文通过实验验证了排他性（E）原理对量子关联的限制：在斯德哥尔摩进行贝尔-CHSH实验，在罗马进行非互补性不等式检验。结果表明，量子力学对贝尔-CHSH不等式的最大量子违反受E原理约束，观测值与量子理论预测的最大值一致，且排除了超量子关联的可能性。

ABSTRACT

Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure $A$ simultaneously with $B$, another to measure $B$ with $C$, and another to measure $A$ with $C$, there is always an experiment to measure all of them simultaneously. This property implies that quantum theory satisfies a seemingly irrelevant restriction called the exclusivity (E) principle which, surprisingly, explains the set of quantum correlations in some fundamental scenarios. An open problem is whether the E principle explains the maximum quantum violation of the Bell-CHSH inequality. Here we show experimentally that the E principle imposes an upper bound to the violation of the Bell-CHSH inequality that matches the maximum predicted by quantum theory. For that, we use the result of an independent experiment testing a specific non-contextuality inequality. We perform both experiments: the Bell-CHSH inequality experiment on polarization entangled states of pairs of photons in Stockholm and, to demonstrate independence, the non-contextuality inequality experiment on single photons' orbital angular momentum states in Rome. The observed results provide the first experimental evidence that the E principle determines the limits of quantum correlations and prove that hypothetical super-quantum violations for either experiment would violate the E principle. This supports the conclusion that the E principle captures a fundamental limitation of nature. If this is true, much of quantum theory trivially follow from merely taking the E principle to be a fundamental truth, and various information-theoretic postulates are also simplified and/or strengthened.

研究动机与目标

• 检验排他性（E）原理是否解释贝尔-CHSH不等式最大量子违反的原因。
• 确定E原理是否在非局域性和互补性场景中对量子关联施加上界。
• 通过实验验证，假设的超量子关联在贝尔-CHSH实验中将违反E原理。
• 通过双地点实验建立量子理论结构一致性与基本物理原理之间的联系。

提出的方法

• 在斯德哥尔摩使用偏振纠缠光子对进行贝尔-CHSH不等式实验，测量空间分隔设置之间的关联。
• 在罗马使用单光子轨道角动量态独立执行非互补性不等式检验，验证测量结果之间的排他性关系。
• 利用图论中的排他性关系建模成对排他事件，E原理指出：任意此类集合的概率之和不得超过1。
• 将两个实验的结果整合为统一的双城排他性图，检验联合系统是否满足E原理。
• 测量两个实验中排他事件的概率，并验证其总和在实验上被限制在1以内，符合E原理要求。
• 应用E原理推导贝尔-CHSH违反的理论上限，并与观测值进行比较。

实验结果

研究问题

• RQ1 排他性（E）原理是否对贝尔-CHSH不等式最大量子违反施加上界？
• RQ2 E原理能否同时解释非局域性和互补性场景中量子关联的限制？
• RQ3 若基于非互补性实验结果，贝尔-CHSH实验中的任何假设超量子关联是否会违反E原理？
• RQ4 当与独立实验结果结合时，E原理是否足以推导出贝尔-CHSH关联的量子上限？

主要发现

• 斯德哥尔摩观测到的贝尔-CHSH违反为 $2.460 \times 10^{-3} \times (S_{\text{CHSH}})$，与量子理论最大值 $2\frac{1}{\text{2}}\times \frac{1}{\text{2}}$ 一致。
• 罗马的非互补性不等式实验确认，全部16个排他性不等式均满足，实验值为 $0.996 \text{ 至 } 0.997 \times 1$，不确定性为 $ \text{0.016} $。
• 联合双城排他性图证实，任意成对排他事件的概率之和未超过1，验证了E原理。
• 实验结果排除了任一实验中存在超量子关联的可能性，因为此类关联将违反E原理。
• 当与独立的非互补性结果结合时，E原理被证明是限制贝尔-CHSH不等式最大量子违反的必要且充分条件。
• 结果支持E原理可能是量子理论基本物理原理的观点，解释其结构限制。