A second-quantised Shannon theory

Thesis

Shannon's theory of information laid the groundwork for the rapid developments in information and communications technologies over the last century. Yet, it assumed that information carriers were described by the laws of classical physics, whilst at the most fundamental level, nature obeys the laws of quantum physics. Quantum Shannon theory, which describes information carriers as quantum states, has led to a new era of possibilities, such as perfectly secure cryptography without pre-established keys. Yet, there is a sense in which this transition from classical to quantum is incomplete. Traditionally, quantum Shannon theory has focused on scenarios where the internal states of information carriers are quantum, whilst their trajectories in spacetime have still been assumed to be classical.

This work presents a second level of quantisation where both the information itself and its propagation in spacetime are treated in a quantum fashion. The second-quantised Shannon theory describes the possibility of a single particle being simultaneously transmitted through multiple communication channels in a quantum superposition. The framework is developed using the tools of higher-order transformations and quantum resource theories, formally quantifying the resources required for communication between a sender and receiver in this setting.

The advantages of the second-quantised theory are illustrated in a series of examples, showcasing various counterintuitive phenomena that occur when information is simultaneously transmitted through multiple communication channels. In particular, when a single particle travels in a quantum superposition through two alternative transmission lines, the noisy processes in the two lines can destructively interfere, leading to a cleaner communication channel overall. Various different scenarios are encompassed in the framework, including transmission through a superposition of both independent and correlated channels, as well as through large-scale communication networks. This work concludes with a study of the robustness of these protocols to errors and a discussion of recent experimental demonstrations of their associated communication advantages.

Authors: Kristjánsson, H

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: superposition of channels; Shannon theory; quantum information; indefinite causal order; quantum circuits; quantum communication; vacuum extension; quantum computation; quantum Shannon theory; time-correlated channels; interference of quantum channels; coherent control; quantum supermaps; higher-order processes; quantum foundations; resource theories
• Subjects: Physics; Quantum computing; Quantum information; Theoretical computer science; Quantum communication; Quantum physics; Theoretical physics; Quantum theory; Mathematical physics; Computer science