Mathematical aspects of continuous variable quantum information

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Quantum information theory seeks to quantitatively asses the potential of quantum-mechanical systems to act as information-processing resources. Relevant operational tasks include the preservation and transmission of classical information as well as quantum states. Corresponding mathematical optimization problems have been identified successfully, but their properties are poorly understood in general. The case of continuous-variable systems, which describe, e.g., fiberoptic communication channels, is particularly relevant operationally, but poses significant mathematical challenges.This project aims to advance quantum information theory with continuous variables. On the one hand, it will help to close the gap between what is known in classical information theory and the setting of quantum information: by finding non-commutative generalizations of classical information-theoretic results, this will shed new light on the generality of the latter. On the other hand, the project will seek to identify intrinsically quantum features, which have applications to e.g., cryptographic protocols. Special emphasis will be placed on the particular technical and operational consequences of dealing with continuous variables as opposed to finite-dimensional systems.