标题： 使用投影Loschmidt回波测量Rényi熵 显示英文标题

标题： Measuring Rényi entropy using a projected Loschmidt echo

摘要： 我们提出高效且实用的协议来测量第二Rényi熵（RE），其指数形式称为纯度。 我们通过建立与Loschmidt回波（LE）类型测量序列的直接联系来实现这一点，该方法适用于量子多体系统。 值得注意的是，我们的方法不依赖于随机噪声平均，这一特性可以扩展到测量时间有序相关函数（OTOCs）的协议中，正如我们所展示的那样。 作为示例，我们表明我们的协议可以在基于超导量子比特的平台以及腔-QED囚禁的超冷气体中实际实现。 显示英文摘要

摘要： We present efficient and practical protocols to measure the second R\'enyi entropy (RE), whose exponential is known as the purity. We achieve this by establishing a direct connection to a Loschmidt echo (LE) type measurement sequence, applicable to quantum many-body systems. Notably, our approach does not rely on random-noise averaging, a feature that can be extended to protocols to measure out-of-time-order correlation functions (OTOCs), as we demonstrate. By way of example, we show that our protocols can be practically implemented in superconducting qubit-based platforms, as well as in cavity-QED trapped ultra-cold gases.