Probing quantum correlations in many-body systems: a review of scalable methods

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.

Automated summary

This review discusses methods for detecting and characterizing quantum correlations in many-body systems, with a focus on scalable approaches. It introduces concepts such as quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality, both in the bipartite scenario and their generalizations to multipartite cases. The review also covers recent progress in characterizing quantum correlations, experimental techniques for preparing and measuring highly-entangled many-body systems, and the challenges associated with each platform. It concludes with a list of open problems in the field.