本项目拟开展Majorana表象在量子多体效应方面的研究，并将其应用于量子信息、超冷原子物理等具体物理系统。具体分为以下三方面：首先，我们将把Majorana表象推广到任意多qubit纯态及混合态。以此为基础，通过Majorana星分布研究多体量子纠缠度量、分类。然后，利用Majorana星的运动方程为手段刻画量子多体演化，得到超越平均场近似的多体动力学描述。同时，结合Bethe Ansatz，得到Majorana星和双阱Bose-Einstein凝聚体等经典冷原子系统能量本征态解析解之间的关系。最后，利用Majorana星构型及其在球面上的曲线方程，给出一套将实验或数值模拟给出的未知量子态表示为典型量子态或其叠加的方法。并将上述方法应用到其他领域的量子多体效应研究，如Fisher信息、拓扑不变量等。研究成果将有助于开拓研究多体量子态纠缠、动力学、相变等量子多体效应的新方法和新手段。

In this project, by taking Majorana representation as main method, we will research on the quantum many body effects, and apply the methods to specific physical systems in the fields of quantum information and ultracold atomic physics. Our research will be divided into the following three aspects: Firstly, we will generalize the Majorana representation to study arbitrary multiqubit pure and mixed state. Based on this, the many body entanglement measurement and classification will be studied by the distribution of the Majorana stars. Secondly, the quantum many body evolutions will be interpreted by the motion equations of Majorana stars, and the many body description beyond the mean field approximation will be derived. Meanwhile, by combining the method of Bethe Ansatz, the relation between the Majorana stars and the analytic solutions of the eigenstate in classical ultracold system, such as double well Bose-Einstein condensates, will be established. At the last, the structure and curve equation of the Majorana stars on the Bloch sphere will develop a new way to transform the unknown quantum state derived by the experiment or numerical simulation into the known typical states or their superpositions. The above method will also be used to study quantum multibody effects in other fields, such as Fisher information, topology invariants and so on. This project will help to develop new methods and new ways to study the quantum many body effect, such as multipartite quantum entanglement, dynamics, and phase transition.