Urías Jesús, Méndez Martínez José Manuel
Instituto de Física, UASLP, San Luis Potosí, SLP, Mexico.
Sci Rep. 2018 May 8;8(1):7128. doi: 10.1038/s41598-018-24970-3.
The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpretation of quantum correlations, without involving information transmission between the parties as to sustain causality), is proposed and resolved exhaustively for the quantum correlations established by a Clauser-Horne-Shimony-Holt setup (or CHSH box). The amount of nonlocality that is available in a CHSH box is measured by its proximity to the nearest Popescu-Rohrlich set of causal stochastic processes (aka a PR box) in the no-signaling polytope, related by polyhedral duality to Bell's correlation function. The proposed amount of average nonlocality is an entanglement monotone with a simple relation to concurrence. We provide the optimal setup vectors of a maximally nonlocal CHSH box for any entangled pair. The strongest nonlocality is the fraction [Formula: see text] of a PR box, attained by maximally entangled qubit pairs. The most economical causal stochastic process reproducing any maximally nonlocal CHSH box is developed. Data produced by a computer implementation of the simulator agrees with the quantum mechanical formulas.
多方量子纠缠态所建立的关联中的关键特征是非局域性。提出了一个用于测量平均非局域性的量，它将非局域性与共享随机性区分开来，并与无信号随机过程直接相关（无信号随机过程为量子关联提供了一种操作解释，且不涉及各方之间的信息传输以维持因果关系），并针对由克劳泽 - 霍恩 - 希莫尼 - 霍尔特装置（或CHSH盒）所建立的量子关联进行了详尽求解。CHSH盒中可用的非局域量通过其在无信号多面体中与最接近的因果随机过程的波佩斯库 - 罗尔利希集（即PR盒）的接近程度来衡量，它通过多面体对偶性与贝尔关联函数相关。所提出的平均非局域量是一种纠缠单调量，与并发度有简单关系。我们给出了任意纠缠对的最大非局域CHSH盒的最优设置向量。最强的非局域性是PR盒的分数[公式：见正文]，由最大纠缠量子比特对达到。开发了重现任何最大非局域CHSH盒的最经济的因果随机过程。模拟器的计算机实现所产生的数据与量子力学公式一致。
