引力理论是物理学研究中最前沿和困难的领域之一，引力的全息性质则是近些年研究的热点。其中利用量子信息的语言以及概念理解量子场论以及量子引力的性质是其中一个重要的方向。本项目拟在该方向深入研究三个相关重要问题：1、量子场论中非定域激发态的纠缠熵的动力学演化，进而讨论场论中的幺正退纠缠算符的性质。2、场论中纯化纠缠的解析计算，以及其全息对偶猜想的证实与证伪。3、几何态的构造，以及定量刻画几何态所需满足的条件。这三个问题对于更精细的理解场论与纠缠的关系和引力的全息性质有重要意义。

Gravity theory is one of the most frontier and difficult research field of physics. Recently, many researchers focus on the holographic properties of gravity theory. One of the most important direction is to study the quantum field theories and quantum gravity theory by using the concepts and methods from quantum information theory. This project aims at studying the following three important problems:1、The non-local excitation in quantum field theory and its dynamic evolution. 2、Analytical evaluation of entanglement of purification in quantum field theory, and prove or disprove the conjecture of its holographic formula. 3、The constructions of geometric states, and the necessary and sufficient conditions on a geometric state. These three problems are significant to understand the relations between entanglement in quantum field theory and the holographic properties of gravity theory.