[论文解读] Quantum nonlocality: How does Nature perform the trick?(1)

Nicolas Gisin|arXiv (Cornell University)|Jan 1, 2009

Quantum Mechanics and Applications参考文献 2被引用 3

一句话总结

本文通过分析空间分隔的量子系统之间的关联，研究了量子非定域性，证明了量子力学预测的关联比任何局域隐变量理论都更强且不可分解。其主要贡献在于表明，量子理论对纠缠系统的完整描述导致了无法用经典关联概念解释的非定域性，挑战了关于定域性和实在性的经典直觉。

ABSTRACT

Since our early childhood we know in our bones that in order to interact with an object we have either to go to it or to throw something at it. Yet, contrary to all our daily experience, Nature is nonlocal: there are spatially separated systems that exhibit nonlocal correlations. In recent years this led to new experiments, deeper understanding of the tension between quantum physics and relativity and to proposals for disruptive technologies. Consider two spatially separated quantum systems, one controlled by Alice, the other by Bob, in a pure state . Alice and Bob may perform some measurements x and y on their systems and collect the results a and b, respectively. This situation is described by a conditional probability distribution p (a,bj x,y). In general this correlation doesn’t factorize: p (a,bj x,y) 6 p (aj x) � p (bj y), i.e. the two systems are correlated. At first, this is no surprise, correlations are everywhere. For example, consider two cups of the same color, either both red or both green, one in Alice’s and one in Bob’s hands. If they looks at the color of their cups, Alice and Bob’s results are correlated. In this example the origin of the correlation is obvious, Alice and Bob had only partial information: they knew that both have the same color, but they ignored which color. This differs deeply from the quantum situation, as quantum theory claims that a pure state provides a complete description of the two systems. This led EPR[2] to believe that quantum theory is incomplete in the same sense as the description ”of the same color” provides only an incomplete description of the color state of the cups.

研究动机与目标

• 理解纠缠系统中量子非定域性的起源与本质。
• 将经典关联（例如共享颜色的杯子）与无法用不完整信息解释的量子关联进行对比。
• 阐明为何即使量子力学对系统的完整描述仍会导致非定域关联，从而挑战EPR关于不完备性的论点。
• 探讨量子力学与相对论在非定域性问题上的基础性矛盾。
• 探讨非定域性对量子技术及量子理论基础解释的启示。

提出的方法

• 分析爱丽丝与鲍勃之间共享的纯纠缠态的两体量子系统。
• 将测量结果a和b建模为在局部测量x和y下的条件概率p(a,b|x,y)。
• 通过因子分解条件p(a,b|x,y) ≠ p(a|x)p(b|y)对比量子关联与经典关联。
• 以EPR佯谬作为概念框架，对比经典隐变量模型与量子力学。
• 强调量子理论提供了完整描述，但仍预测出非定域关联。
• 指出非定域性并非源于信息不完整，而是源于量子态的内在结构。

实验结果

研究问题

• RQ1 为何即使系统被纯态完全描述，量子系统仍表现出非定域关联？
• RQ2 基于共享信息的量子非定域性与经典关联在根本上如何不同？
• RQ3 量子态描述的完备性在产生非定域性中起什么作用？
• RQ4 EPR论点为何无法排除量子力学中的非定域性？
• RQ5 非定域性在量子理论中的基础性与技术性影响是什么？

主要发现

• 即使量子态是系统完整描述，量子非定域性依然出现，这与经典直觉相悖。
• 量子力学中的非定域关联无法用共享的经典信息或隐变量解释。
• 因子分解失败p(a,b|x,y) ≠ p(a|x)p(b|y)是非定域性的标志，而非知识不完整的表现。
• EPR论点假设非定域性意味着不完备性，在量子力学中并不成立。
• 量子非定域性是自然的基本特征，而非理论缺陷的标志，且是新兴量子技术的基础。
• 本文确立了非定域性是量子力学的内在属性，即使在完整态描述下依然存在。