AI 中文总结
该研究探讨共享随机性受限的贝尔非局域性经典模型，通过评估线性贝尔泛函刻画无共享随机性的关联，扩展至量子网络时构建非线性不等式，还将其应用于生成有限共享随机性二分场景的熵型贝尔不等式。
AI 中文摘要
贝尔非局域性揭示了无法用经典模型解释的关联，在量子信息理论中占据核心地位。本研究探讨了共享随机性受限情况下的贝尔非局域性经典模型：在有界共享随机性的 bipartite（二分）场景中，经典关联集变为非凸；通过同时评估多个线性贝尔泛函，刻画了无共享随机性时可实现的关联。随后将分析扩展至量子网络，放宽了源独立性的标准假设，此时二分场景推导的可行性约束可用于认证源相关性，还构建了非线性不等式，以区分含相关源的经典模型与标准量子网络中可实现的关联。作为应用，证明这些非线性网络不等式能在有限共享随机性的二分场景中产生熵型贝尔不等式。
英文摘要
Bell nonlocality reveals correlations that cannot be explained by classical models and plays a central role in quantum information theory. In this work, we investigate classical models of Bell nonlocality under restrictions on shared randomness. For bipartite scenarios with bounded shared randomness, the set of classical correlations becomes nonconvex. We characterize the correlations achievable without shared randomness through the simultaneous evaluation of multiple linear Bell functionals. We then extend our analysis to quantum networks by relaxing the standard assumption of source independence. In this setting, the feasibility constraints derived for the bipartite case can be used to certify source dependence, and we further construct nonlinear inequalities that distinguish classical models with correlated sources from correlations achievable in standard quantum networks. As an application, we show that these nonlinear network inequalities give rise to an entropic Bell inequality for bipartite scenarios with limited shared randomness.
Comments10 pages, 4 figures
