Patra Soumyadip, Bierhorst Peter
Department of Mathematics, University of New Orleans, New Orleans, LA 70148, USA.
Entropy (Basel). 2023 Sep 2;25(9):1291. doi: 10.3390/e25091291.
The probability estimation framework involves direct estimation of the probability of occurrences of outcomes conditioned on measurement settings and side information. It is a powerful tool for certifying randomness in quantum nonlocality experiments. In this paper, we present a self-contained proof of the asymptotic optimality of the method. Our approach refines earlier results to allow a better characterisation of optimal adversarial attacks on the protocol. We apply these results to the (2,2,2) Bell scenario, obtaining an analytic characterisation of the optimal adversarial attacks bound by no-signalling principles, while also demonstrating the asymptotic robustness of the PEF method to deviations from expected experimental behaviour. We also study extensions of the analysis to quantum-limited adversaries in the (2,2,2) Bell scenario and no-signalling adversaries in higher (n,m,k) Bell scenarios.
概率估计框架涉及直接估计在测量设置和辅助信息条件下结果出现的概率。它是在量子非局域性实验中验证随机性的有力工具。在本文中，我们给出了该方法渐近最优性的自包含证明。我们的方法改进了早期结果，以便更好地刻画针对该协议的最优对抗性攻击。我们将这些结果应用于(2,2,2)贝尔场景，得到了由无信号原理约束的最优对抗性攻击的解析刻画，同时也证明了概率估计框架方法对偏离预期实验行为的渐近鲁棒性。我们还研究了将分析扩展到(2,2,2)贝尔场景中的量子受限对手以及更高(n,m,k)贝尔场景中的无信号对手。
