[论文解读] The Universality of Non-Local Boxes

Manuel Förster, Stefan Wolf|arXiv (Cornell University)|Aug 5, 2008

Quantum Mechanics and Applications被引用 3

一句话总结

本文证明，无论其复杂性如何，任何非局域相关性都可以通过非局域盒这一非局域性的基本单元，以任意接近的程度进行近似。作者通过展示这些盒子可通过组合与概率混合来模拟任何非局域行为，从而确立了其普遍性，解决了佩罗斯基与罗尔里希提出的一个开放性问题。

ABSTRACT

Abstract. One of the most fascinating consequences of quantum theory is non-locality, i.e., the fact that the behavior under measurements of (spatially separated) parts of a system can have a correlation unexplainable by shared classical information. Note that at the same time, these correlations are nonsignaling and do not allow for message transmission. Popescu and Rohrlich have defined a non-local box as a “basic building block of non-locality ” and initiated a systematic study of non-local correlations and their applications. They left open, however, whether any non-signaling correlation can be simulated by such non-local boxes. We show that the answer is yes with respect to arbitrarily accurate approximations. 1 Motivation and Main Result When two parts of a quantum state are separated and, later, measured, then the outcomes can be correlated. In probability theory, the term correlation is often used to indicate a departure from independence. The correlations we address in this note are of a stronger kind, namely unexplainable even by shared randomness. More precisely, we study correlations between the joint behavior of the two ends of a bi-partite input-output system, characterized by a conditional probability distribution P(ab|xy), where x and a stand for the input and output on the left-hand side of the system, and y and b for the corresponding values on the right-hand

研究动机与目标

• 确定非局域盒是否可在量子基础中模拟任意非局域相关性。
• 解决佩罗斯基与罗尔里希关于非局域盒普遍性的一个开放性问题。
• 确立任意非局域相关性可仅通过非局域盒以足够高的精度进行近似。
• 通过非局域盒的组合与概率组合，形式化一般非局域相关性的模拟过程。

提出的方法

• 作者将非局域盒定义为一种生成具有最大非局域性的非局域相关性的原始资源。
• 他们通过非局域盒的概率混合与组合来构建更复杂的相关性。
• 该方法依赖于证明：任何满足非局域条件的条件概率分布 P(ab|xy) 均可近似为极值非局域盒的凸组合。
• 该构造利用凸几何技术以及非局域多面体的结构，以证明其近似密度。
• 该证明利用了非局域盒在概率混合下可生成整个非局域相关性空间的事实。

实验结果

研究问题

• RQ1 是否可仅通过非局域盒模拟任意非局域相关性？
• RQ2 非局域盒集合是否普遍适用于近似所有非局域相关性？
• RQ3 模拟任意非局域行为所需的最小资源是什么？
• RQ4 非局域盒能以多高精度近似一般非局域相关性？

主要发现

• 任何非局域相关性均可仅通过非局域盒以任意精度进行近似。
• 该近似通过极值非局域盒的凸组合实现，从而证明了该资源的普遍性。
• 该结果证实，非局域盒在操作框架下构成了模拟所有非局域相关性的完整基。
• 该构造表明，实现普遍模拟无需额外的非局域资源，仅需非局域盒即可。