本项目以量子信息为背景，以算子论和算子代数为基本理论框架，采用算子代数保持问题的研究方法和技巧，从不变量角度出发，研究保持态的物理特性的映射。研究内容和目标如下：对量子信息中态的物理特性如可分性，纠缠性等进行数学表征，利用算子的特征或者代数性质刻画态的物理特性，并将其作为态空间的不变量。进而利用希尔伯特空间的几何结构和算子代数理论分析保持以上不变量映射的存在性。最后采用算子代数中保持问题的方法和技巧结合保持问题已有的研究结果刻画保持以上不变量映射的特征。以期利用此保持映射的特征来判断物理态的性质，或者判断态空间的不变量是否能够决定态的其他性质，从而将研究对象从态空间缩小到不变量上。本项目的研究成果不仅为量子信息研究提供理论基础，开创新的研究思路和方法，同时能够促进算子代数的发展，丰富算子代数理论的研究成果，具有非常重要的理论意义。

This project is based on the background of quantum information. It use theoperator theory and operator algebras theory as the theoretical framework. From the perspective of the essential invariants, this project studies the mappings preserving the physical properties of states using the methods and techniques of linear preserver problems. The content and objectives of the study are as follows. We characterize the physical properties of states in terms of operator theory or algebraic structure which are used as the invariants of the state space. By using the eometric structure of Hilbert space and the operator algebras theory we study the existence of the preserving mappings further. Finally, we use the methods, techniques and results of preserving problems in operator algebras to describe the features of the mappings. We hope to use this feature of the preserving mappings to determine the properties of states, or whether the essential invariants of state space determines the other roperties of states, as the research object narrow from all the state space to the essential invariants. The research results will not only provide a eoretical basis and open up new ideas and methods for the research of quantum information but also promote the development of operator algebras which has very important theoretical significance.