Accessible Quantifiers of Multipartite Entanglement in Atomic Systems

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The characterization and classification of multipartite entanglement is crucial for the investigation of many-body systems, foundational problems and quantum technologies. A central goal is to discover robust, experimentally accessible criteria to witness and explore the many facets of quantum correlations. Multipartite entanglement provides formidable challenges arising from the exponential increase of the HIlbert space dimension with the number of the quantum system constituents. For instance, the full classification of multipartite entanglement is missing in the literature, and the possibility to witness the classes of entangled states allowing quantum advantages in different quantum information applications is still largely unexplored.This collaboration puts together several European leading groups that have extensive experience in studying bipartite entanglement and in manipulation of quantum matter. Here we intend to focus our efforts on the study of the multipartite case. The experimental groups have substantial infrastructure permitting the use of ultra-cold atoms and their detection. The techniques include: coherent spin manipulation, atom chips, Bose-Einstein condensates, atom interferometry and arrays of optical tweezers. The experimental groups have already developed powerful atom detection techniques with: high quantum efficiency, a capacity for multiple atom detection, higher order correlations and good spatial resolution, all of which will be used to develop experimental protocols for witnessing multipartite entanglement. A crucial asset in the project is the dedicated collaboration of two theoretical groups to guide the exploration of the many possible experimental strategies to make these characterizations. The high degree of experimental control and detection efficiencies will permit the evaluation of the Fisher information and other multipartite entanglement witnesses based on the measurement of collective variables with unprecedented accuracies. Important efforts will be dedicated to investigate novel quantifiers specifically tailored to the experimental platforms created in this project which will bring a novel classification of multipartite entanglement based on the Dyson rank. The successful completion of this project will provide to the community a deeper understanding of multipartite entanglement and its relation with fundamental and technological applications.