A second-quantized Shannon theory

Abstract

Shannon’s theory of information was built on the assumption that the information carriers were classical systems, carrying classical messages and moving along well-defined trajectories. Its quantum counterpart, quantum Shannon theory, explores scenarios in which the messages can be quantum, but their trajectories are still classical. Quantum Shannon theory can be regarded as a first quantisation of Shannon’s information theory, where the internal state of the information carriers is quantised, but the motional degrees of freedom are treated as classical. In this talk I will discuss a second level of quantisation, where not only the information carriers, but also the path along which information travels can be in a quantum superposition. I will present several examples of this extended scenario, discussing different ways in which second-quantised communication protocols can achieve tasks that are impossible in conventional quantum Shannon theory.