We review methods that allow one to detect and characterize quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without requiring a number of measurements or computational resources to analyze the data that scale exponentially with the system size. We begin with introducing the concepts of quantum entanglement, Einstein–Podolsky–Rosen steering, and Bell nonlocality in the bipartite scenario, to then present their multipartite generalization. We review recent progress on characterizing these quantum correlations from partial information on the system state, such as through data-driven methods or witnesses based on low-order moments of collective observables. We then review state-of-the-art experiments that demonstrate the preparation, manipulation and detection of highly-entangled many-body systems. For each platform (e.g. atoms, ions, photons, superconducting circuits) we illustrate the available toolbox for state preparation and measurement, emphasizing the challenges that each system poses. To conclude, we present a list of timely open problems in the field.

中文翻译：

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探测多体系统中的量子相关性：可扩展方法的回顾


我们回顾了允许人们检测和表征多体系统中量子相关性的方法，特别关注可扩展的方法。即，那些适用于具有多个自由度的系统，不需要大量测量或计算资源来分析随系统规模呈指数级扩展的数据。我们首先介绍二分场景中的量子纠缠、爱因斯坦-波多尔斯基-罗森转向和贝尔非定域性的概念，然后介绍它们的多分概括。我们回顾了从系统状态的部分信息来表征这些量子相关性的最新进展，例如通过数据驱动的方法或基于集体可观测量的低阶矩的见证。然后，我们回顾了最先进的实验，这些实验展示了高度纠缠的多体系统的准备、操纵和检测。对于每个平台（例如原子、离子、光子、超导电路），我们说明了用于状态准备和测量的可用工具箱，强调每个系统带来的挑战。最后，我们列出了该领域及时解决的问题。