纠缠破坏信道与量子测量的代数结构与几何特征

项目名称： 纠缠破坏信道与量子测量的代数结构与几何特征

项目编号： No.11201329

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 贺衎

作者单位： 太原理工大学

项目金额： 22万元

中文摘要： 量子信息学是一门数学、物理学与计算机科学相交叉的学科,已成为当今最热门的研究领域之一.近年来算子理论与算子代数学者从自身学科优势出发去研究量子信息学中的问题,已成为这个研究领域的新亮点.量子信道与量子测量是量子信息学中的基本概念.从算子理论的角度看,量子信道是迹类算子空间上保迹的完全正线性映射,量子测量是量子态集合上的一类保凸结构映射.探讨量子测量与各类量子信道的结构与性质是量子信息学中的基本课题,也是重要的算子理论与算子代数课题.本申请项目拟研究一类重要的量子信道,即纠缠破坏信道在无限维情形的算子和表示及由此类信道组成的凸集端点的刻画问题.引入零化Discord信道的概念,探讨其算子和表示的刻画问题及其与纠缠破坏信道的关系.研究量子态集合与可分态集合上保逆凸双射的刻画问题,揭示此类映射与量子测量的关系.本项目将从新的角度获得对纠缠破坏信道与量子测量结构的新信息以及对相关算子结构的新认识.

中文关键词： 正迹类算子；纠缠破坏信道；量子测量；保凸组合映射；量子效应代数同构

英文摘要： Quantum information science, which is an interdisciplinary science involving mathematics, physics and computer science, is one of the most intriguing fields. In recent years, many scholars in operator theory and operator algebras devote to solving some open problems in quantum information theory by operator theoretical approaches. Quantum channels and quantum measurements are fundamental concepts in quantum information theory. From an operator theory point of view, a quantum channel is a completely positive and trace preserving linear map on the trace class operators, and a quantum measurement is a convexity preserving map on the convex set of quantum states. The research on structures and features of quantum channels and quantum measurements is one of fundamental problems in quantum information theory, and also is an important problem in the operator theory. This project will be devoted to giving a characterization of the operator sum representation of a kind of important quantum channels, entanglement breaking channels, for the infinite dimensional quantum systems and giving a characterization of extreme points of the convex set of all entanglement breaking channels in arbitrary dimensional case. In the project, we will devote to giving a concept of discord annihilating channels, and giving a characterization

英文关键词： Postive trace class operators；Entanglement breaking channels；Quantum measurement；Maps preserving convex combinations；Isomorphism on quantum effects