算子代数是研究量子物理的重要工具，物理学的实际问题为算子代数理论注入新的研究课题。在多体量子系统中，状态空间由多个Hilbert空间的张量积描述，其结构具有多体非局域的复杂性，其纠缠态是量子信息科学中的重要资源，但却不容易判断。因此有必要研究多体量子系统的对称性和量子纠缠判据。本项目拟用算子代数研究经典Wigner定理在多体量子系统中的推广问题；研究一类可以识别纠缠态的积态正线性映射；以及研究相关算子代数上具有张量积结构不变量的映射问题。本项目具算子代数与量子信息科学相结合的提出与解决问题的特色。使用的研究方法体现量子系统从单体到多体的复合过程；拟给出多体系统中使积态跃迁概率不变的对称，积态强正线性映射结构，并由此给出多体纠缠的一种分类依据，以及相关内容在算子代数中的数学推广。本项目期望: 在多体量子系统中建立基本的对称性理论，发展积态正线性映射理论，丰富多体系统中保持不变量的映射理论。

Operator algebra is an important tool for the study of quantum physics, and the practical problems of physics provide new research issues for operator algebras. In Multipartite Quantum Systems (MQS for short), the state spaces are described by tensor product of Hilbert spaces. Its structure is of multipartite nonlocal complexity, and its entanglement is the important resource in quantum information science. However, it is not easy to detect. Therefore, it is necessary to study the symmetry and the entanglement criterion in MQS. This project intends to discuss the generalization of classical Wigner's theorem to MQS by using operator algebra; to study on a class of the positive linear maps on product states, by which the entanglement can be identified; to study the preserver problem related to quantum information science on operator algebras. This project possesses the special feature of raising and solving problems from the combination with operator algebra and quantum information science. The methods used in the study exhibit the composite process from single to multipartite systems. In order to show the symmetry preserving the transition probability in MQS, the structure of strong linear maps positive on product states, by which a classification basis of entanglement in MQS is obtained and a mathematical generalization for the related content in operator algebra. This project is expected to develop fundamental symmetry theory in MQS and the theory of linear maps positive on product states, and enrich the theory of preserver problem in MQS as well.