Non-commutative analysis of non-local games and quantum security

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Quantum entanglement is a central notion in quantum information theory and a key resource in the applications that are driving efforts to develop quantum technologies. While there is a growing depth of understanding of the concept and its many potential uses, the theory of quantum entanglement remains an active, challenging, and fundamental area of investigation in quantum science.Non-local games provide an insightful platform on which to quantify entanglement as a resource for communication and to analyze the security of encryption protocols. The theory of non-local games recently revealed profound connections between quantum entanglement and non-commutative analysis. These connections together with the plethora of applications in quantum cryptography have motivated a current global effort to develop the theory and applications of non-local games in quantum information science. The proposed research will significantly contribute to this effort by (1) establishing new quantitative tools from non-commutative analysis to measure bipartite entanglement as a resource, and (2) developing novel methods to improve the security analysis of uncloneable encryption protocols. The collaboration between Carleton University, the University of Delaware and Chalmers University of Technology (Gothenburg) will strengthen Canada's leadership in the operator theoretic approach to non-local games as well as uncloneable encryption. It will also set the stage for subsequent collaborations and novel applications in quantum cryptography.