Applied Operator Algebra Theory

应用算子代数理论

• 批准号: 1201886
• 负责人: Marius Junge
• 金额: $ 24.7万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-15 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201886&HistoricalAwards=false
• 关键词: Applied; Operator; Algebra; Theory

The aim of the first part of the project is to redevelop Kirchberg WEP and QWEP theory over a coefficient algebra. The staring point is a detailed analysis of the scalar theory and a suitable adaption of the operator-valued version using tensor norms. The second part of the project concerns improved martingale inequalities for continuous time filtrations which has applications to semigroup theory and is related to problems in compressed sensing.One of the aims of this proposal is to combine cutting edge research in mathematics with experimental research in Quantum Information Theory. Although still in a developing phase Quantum Information Theory can become an important tool in providing secure keys for communication. Some aspects of this proposal are concerned with the theoretical background calculating the security rates and quantum advantages. As long as testing quantum computers is difficult, the theoretical approach has to take the lead in exploring possibilities and constraints. This work is highly interdisciplinary (experimental physics and computer science) and has the potential to make contribution to more secure information through the use of quantum mechanical tools. In this information based society this can become relevant.

该项目第一部分的目标是在系数代数上重新开发 Kirchberg WEP 和 QWEP 理论。出发点是对标量理论的详细分析以及使用张量范数对算子值版本的适当调整。该项目的第二部分涉及连续时间过滤的改进鞅不等式，该不等式适用于半群理论，并与压缩感知问题相关。该提案的目的之一是将数学的前沿研究与量子信息的实验研究结合起来理论。尽管仍处于发展阶段，量子信息论可以成为提供安全通信密钥的重要工具。该提案的某些方面涉及计算安全率和量子优势的理论背景。只要测试量子计算机很困难，理论方法就必须带头探索可能性和限制。 这项工作是高度跨学科的（实验物理学和计算机科学），并且有潜力通过使用量子力学工具为更安全的信息做出贡献。在这个以信息为基础的社会中，这可能变得有意义。