A second-quantised Shannon theory
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Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities that arise when the information carriers are quantum particles. Traditionally,quantum Shannon theory has focussed on scenarios where the internal state of the particles is quantum, while their trajectory in spacetime is classical. Here we propose a second level of quantisation where both the information and its propagation in spacetime is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the couterintuitive phenomena taking place when information travels in a superposition of paths.
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