Quantum Shannon theory with superpositions of trajectories

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 arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space-time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.