Accessible Quantifiers of Multipartite Entanglement in Atomic Systems

多体纠缠的表征和分类对于多体系统、基础问题和量子技术的研究至关重要。一个中心目标是发现强大的，实验上可访问的标准，以见证和探索量子相关性的许多方面。多体纠缠提供了巨大的挑战所产生的希尔伯特空间维数的指数增加的量子系统成分的数量。例如，文献中缺少对多体纠缠的完整分类，而在不同的量子信息应用中见证量子优势的纠缠态类别的可能性仍然很大程度上未被探索。这次合作汇集了几个在研究二体纠缠和操纵量子物质方面拥有丰富经验的欧洲领先团队。在这里，我们打算集中精力研究多方情况。实验组拥有大量的基础设施，可以使用超冷原子并进行探测。这些技术包括：相干自旋操纵、原子芯片、玻色-爱因斯坦凝聚、原子干涉和光镊阵列。实验组已经开发出强大的原子探测技术，具有高量子效率，多原子探测能力，高阶相关性和良好的空间分辨率，所有这些都将用于开发见证多体纠缠的实验协议。该项目的一个重要资产是两个理论小组的专门合作，以指导探索许多可能的实验策略来进行这些表征。高度的实验控制和检测效率将允许评估的费舍尔信息和其他多体纠缠证人的基础上测量的集体变量与前所未有的准确性。重要的努力将致力于研究专门为该项目中创建的实验平台量身定制的新量词，这将带来基于Dyson秩的多体纠缠的新分类。该项目的成功完成将使社区更深入地了解多体纠缠及其与基础和技术应用的关系。

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.