标题： 解析延拓随机测量工具箱 显示英文标题

标题： Analytically Continuing the Randomized Measurement Toolbox

摘要： 我们开发了一种框架，通过解析延拓的方法，在随机测量实验中提取密度矩阵的非多项式解析函数。这种方法被称为稳定解析延拓（SAC），其核心优势在于对量子实验有限次重复产生的统计噪声具有鲁棒性，使其非常适合实际的量子硬件。作为演示，我们使用SAC从通过随机测量协议估计的Rényi熵中估算出数值模拟的淬火Néel态的冯·诺依曼纠缠熵。随后，我们将该方法应用于一个囚禁离子量子模拟器的实验Rényi数据，提取不同演化时间下的子系统冯·诺依曼熵。最后，我们简要指出，SAC框架很容易推广以获得其他非线性诊断工具，例如对数negativity和Rényi相对熵。 显示英文摘要

摘要： We develop a framework for extracting non-polynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic continuation (SAC), is its robustness to statistical noise arising from finite repetitions of a quantum experiment, making it well-suited to realistic quantum hardware. As a demonstration, we use SAC to estimate the von Neumann entanglement entropy of a numerically simulated quenched N\'eel state from R\'enyi entropies estimated via the randomized measurement protocol. We then apply the method to experimental R\'enyi data from a trapped-ion quantum simulator, extracting subsystem von Neumann entropies at different evolution times. Finally, we briefly note that the SAC framework is readily generalizable to obtain other nonlinear diagnostics, such as the logarithmic negativity and R\'enyi relative entropies.