Applied Operator Algebra Theory

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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.