It is well-known that in a Bell experiment, the observed correlation between measurement outcomes – as predicted by quantum theory – can be stronger than that allowed by local causality, yet not fully constrained by the principle of relativistic causality. In practice, the characterization of the set $Q$ of quantum correlations is carried out, often, through a converging hierarchy of outer approximations. On the other hand, some subsets of $Q$ arising from additional constraints [e.g., originating from quantum states having positive-partial-transposition (PPT) or being finite-dimensional maximally entangled (MES)] turn out to be also amenable to similar numerical characterizations. How, then, at a quantitative level, are all these naturally restricted subsets of nonsignaling correlations different? Here, we consider several bipartite Bell scenarios and numerically estimate their volume relative to that of the set of nonsignaling correlations. Within the number of cases investigated, we have observed that (1) for a given number of inputs $n_s$ (outputs $n_o$), the relative volume of both the Bell-local set and the quantum set increases (decreases) rapidly with increasing $n_o$ ($n_s$) (2) although the so-called macroscopically local set $Q_1$ may approximate $Q$ well in the two-input scenarios, it can be a very poor approximation of the quantum set when $n_s$$\gt$$n_o$ (3) the almost-quantum set $\tilde{Q}_1$ is an exceptionally-good approximation to the quantum set (4) the difference between $Q$ and the set of correlations originating from MES is most significant when $n_o=2$, whereas (5) the difference between the Bell-local set and the PPT set generally becomes more significant with increasing $n_o$. This last comparison, in particular, allows us to identify Bell scenarios where there is little hope of realizing the Bell violation by PPT states and those that deserve further exploration.

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非信号相关性的自然受限子集：典型性和收敛性

众所周知，在贝尔实验中，观察到的测量结果之间的相关性——正如量子理论所预测的那样——可能比局部因果关系所允许的要强，但并未完全受到相对论因果关系原理的约束。在实践中，量子相关性的集合 $Q$ 的表征通常是通过外部近似的收敛层次来进行的。另一方面，由附加约束引起的 $Q$ 的某些子集 [例如，源自具有正部分转置 (PPT) 或有限维最大纠缠 (MES) 的量子态] 也适用于类似的数值表征。那么，在定量水平上，所有这些自然受限的非信号相关子集有何不同？这里，我们考虑了几个二分贝尔场景，并在数值上估计了它们相对于一组非信号相关性的体积。在调查的案例数量中，我们观察到（1）对于给定数量的输入 $n_s$（输出 $n_o$），贝尔局部集和量子集的相对体积随着增加 $n_o$ ($n_s$) (2) 虽然所谓的宏观局部集合 $Q_1$ 在双输入场景下可能很好地逼近 $Q$，但当 $n_s $$\gt$$n_o$ (3) 几乎量子集 $\tilde{Q}_1$ 是量子集 (4) $Q$ 与源自当 $n_o=2$ 时，MES 最显着，而 (5) Bell-local 集和 PPT 集之间的差异通常随着 $n_o$ 的增加而变得更加显着。尤其是最后一个比较，使我们能够确定通过 PPT 状态实现贝尔违反的希望很小的贝尔场景以及值得进一步探索的那些场景。