AI 中文总结
研究后选择下CHSH算符反常弱值作为非局域关联的广义界，发现后选择和纠缠是不同资源，纠缠是超越可分离后选择界的关键，并给出纠缠见证协议。
AI 中文摘要
贝尔不等式的违反是纠缠的标志，只有纠缠态能在标准贝尔测试中超越经典界限。本文分析预选择和后选择(PPS)量子系综中CHSH算符的反常弱值，将其视为后选择下贝尔型非局域关联的广义界。固定预选和后选态的重叠，我们比较三种场景：无限制边界态、一个可分离边界态、两个边界态均可分离。对每种情况，我们推导固定贝尔算符的最大弱值以及进一步优化所有CHSH算符得到的最大界。结果表明，后选择和纠缠是不同的操作资源：单独后选择可增强关联，但纠缠是超越相应可分离PPS界所必需的，且两者结合产生最强的可达关联。我们进一步证明，超越可分离界的增强与优化界的态的并发度紧密相关，识别纠缠为额外关联强度的来源。最后，我们展示非局域弱值提供后选择的纠缠见证，并给出一个构造性协议，在理想态自适应设置中检测每个具有非零并发度的纯两比特源态，即使在相应标准CHSH纠缠测试不确定的区域。在该态自适应设置中，我们明确构造了实现与可分离PPS界最大可能分离的后选择和CHSH测量。更广泛地，我们的结果激励结合后选择和纠缠的混合协议，可能应用于改进量子传感、弱值放大和量子信息处理。
英文摘要
Violations of Bell inequalities are a hallmark of entanglement, with only entangled states capable of exceeding classical bounds in standard Bell tests. Here we analyze anomalous weak values of the CHSH-Bell operator in pre- and post-selected (PPS) quantum ensembles, using them to define separability-constrained bounds on Bell-type nonlocal correlations in the presence of post-selection. Fixing the overlap between the pre- and post-selected states, we compare three scenarios: unrestricted boundary states, one separable boundary state, and both boundary states separable. For each case, we derive both the maximal weak value for a fixed Bell operator and the maximal bound obtained by further optimizing over all CHSH operators. Our results show that post-selection and entanglement are distinct operational resources: post-selection alone can enhance correlations, but entanglement is necessary to exceed the corresponding separable PPS bounds, and their combination yields the strongest attainable correlations. Thus the separable PPS bound plays the role of a post-selected separability benchmark, distinct from the standard Bell bound. We further show that the enhancement beyond the separable bound closely tracks the concurrence of the states that optimize the bounds, identifying entanglement as the source of the additional correlation strength. Finally, we show that nonlocal weak values provide post-selected entanglement witnesses, and we give a constructive protocol that detects every pure two-qubit source state with nonzero concurrence in the ideal state-adapted setting, even in regimes where the corresponding standard CHSH entanglement test is inconclusive. More broadly, our results motivate hybrid protocols that combine post-selection and entanglement, with possible applications to improved quantum sensing, weak-value amplification, and quantum information processing.
