量子信息理论中的几个数学问题

Several mathematical problems in quantum information theory

20世纪80年代以来,量子通信理论和技术成为信息领域的热门研究课题.本文综述量子信息理论中一些数学问题的研究进展,特别强调组合数学(包括图论)、数论、代数学和代数几何(有限域上代数曲线的算术理论)在研究量子测量和量子纠错等问题中所起的作用.

The theory of quantum communication and technology have been one of hot research topics in information science and technology since 1980＇s. In this paper, we survey some research development of several mathematical problems in quantum information theory. Particularly, we focus on the important role of combina- torics （including graph theory）, number theory, algebra and algebraic geometry （the arithmetic theory of algebraic curves over finite field） in investigating Quantum measurement and ouantum error-correction.