离散时间正规鞅是一类重要的鞅，离散时间正规鞅的泛函亦具有丰富的分析和代数结构。本项目旨在构建基于离散时间正规鞅泛函的无穷维量子随机分析模型，发展相应的理论与方法，并着重研究它们在量子动力系统半群理论和量子信息理论中的应用。本项目的研究内容涉及数学和物理的众多分支，综合程度高、相互交叉性强。其突出特色在于：我们所要构建的量子随机分析模型是一种具有离散背景的模型，因而适合于通过计算机直接进行相关计算，同时也适合于描述和解决离散形式的应用问题。

Discrete-time normal martingales play an important role in many theoretical and applied fields. And their functionals also have rich analytic and algebraic structures. The project aims to construct a type of infinitely dimensional models of quantum stochastic calculus based on functionals of discrete-time normal martingales, develop the corresponding theries and methods and apply them to quantum dynamical semigroups and quantum information theory. The project strongly involves many research branches in mathematics and physics. Its most striking feature lies in the following observations. We will be devoting ourselves to constructing models with a discrete background, which will be suitable for direct computation by computor and describing peoblems with a discrete background.