The characterization of the extremal points of the set of quantum correlations has attracted wide interest. In the simplest bipartite Bell scenario, a necessary and sufficient criterion for identifying extremal correlations has recently been conjectured, but extremality of tripartite correlations is not well known. In this study, we analyze tripartite extremal correlations in terms of the conjectured bipartite extremal criterion, and we demonstrate that the bipartite part of some extremal correlations satisfies the bipartite criterion, even though they violate Svetlichny’s inequality, and therefore are considered (stronger) genuine tripartite nonlocal correlations. This phenomenon arises from the fact that the conjectured extremal criterion is automatically satisfied when the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality exceeds a certain threshold, the value of which is given by the maximum CHSH violation at the edges of the probability space. This also suggests the possibility that the extremality of bipartite correlations can be certified by verifying whether the CHSH violation exceeds the threshold.

中文翻译：

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二部极值对真正三部相关性的量子极限

这组量子相关性的极值点的表征引起了广泛的兴趣。在最简单的二分贝尔情景中，最近推测了识别极值相关性的必要且充分的标准，但三方相关性的极值性尚不为人所知。在这项研究中，我们根据推测的二部极值准则分析三部极值相关性，我们证明了一些极值相关性的二部部满足二部准则，即使它们违反了 Svetlichny 不等式，因此被认为是（更强）真正的三部非局部相关性。这种现象源于这样一个事实，即当违反 Clauser-Horne-Shimony-Holt (CHSH) 不等式超过某个阈值时，自动满足推测的极值标准，该阈值由边缘处的最大 CHSH 违反给出。概率空间。这也表明可以通过验证 CHSH 违规是否超过阈值来证明二分相关性的极值性。