This research is set in the context of mathematical models related to the quantum mechanical foundations of quantum computing and quantum information theory. The project focuses on the quantification and characterization of entanglement, the key property distinguishing the quantum mechanical model of computation from the classical model. The major theme of the research is to exploit the inherent geometry of the model in order to classify and quantify different kinds of entanglement, to provide criteria for the detection of entangled quantum states, and to motivate and refine new mathematical techniques for the study of quantum information theory.
Continued reduction of the size of components in computers necessarily leads to a consideration of quantum mechanical effects and, potentially, to the development of a computer that can solve problems inaccessible to current technology. An important aspect of developing the required technology is the detection and measurement of putatively entangled states in the laboratory. A key goal of this project is to relate the mathematical theory directly to the design of laboratory protocols for the detection of such entanglement. In addition, greater insight into the nature of entanglement will suggest both new experiments and different approaches to issues of quantum computation and quantum communication.
