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

TL;DR

This review discusses scalable methods for detecting and characterizing quantum correlations in many-body systems, emphasizing approaches that do not require exponential resources, and covers theoretical concepts, experimental platforms, and open challenges.

Contribution

It provides a comprehensive overview of scalable techniques for probing quantum correlations in large many-body systems, integrating theoretical, experimental, and data-driven approaches.

Findings

Recent progress in partial information methods

Experimental demonstrations across various platforms

Identification of open problems in scalable quantum correlation detection

Abstract

We review methods that allow one to detect and characterise 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 generalisation. 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 demonstrated 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.