Applied Operator Algebra Theory

该项目第一部分的目的是在系数代数上重新发展Kirchberg WEP和QWEP理论。起始点是对标量理论的详细分析，以及使用张量范数对算子值形式的适当适应。该项目的第二部分是关于连续时间过滤的改进的鞅不等式，它在半群理论中有应用，并且与压缩意义上的问题有关。该建议的目的之一是将数学的前沿研究与量子信息论的实验研究相结合。尽管量子信息论仍处于发展阶段，但它可以成为为通信提供安全密钥的重要工具。这一提议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是困难的，理论方法就必须率先探索可能性和约束。这项工作是高度跨学科的(实验物理和计算机科学)，并有可能通过使用量子力学工具来为更安全的信息做出贡献。在这个以信息为基础的社会中，这一点可能变得相关。

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.