Localised Systems in Relativistic Quantum Information

TL;DR

This thesis explores localized quantum systems in relativistic quantum information, analyzing cavity models, Dirac fields, and Unruh-DeWitt detectors to understand their behavior under motion and interactions.

Contribution

It introduces new methods for modeling localized quantum fields and detectors in relativistic settings, advancing understanding of quantum information in curved spacetime.

Findings

Cavity motion modeled with Bogoliubov transformations affects quantum states.

Dirac field entanglement varies with motion, showing robustness of certain states.

Non-point-like detectors influence field interactions, enabling advanced state dynamics.

Abstract

This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are useful for quantum information. It draws from many well established physical theories such as quantum field theory in curved spacetimes, quantum optics and Gaussian state quantum information. The results are split between three chapters. For the first results, we set-up the basic framework for working with quantum fields confined to cavities. By considering the real Klein-Gordon field, we describe how to model the non-uniform motion of a rigid cavity through spacetime. We employ the use of Bogoliubov transformations to describe the effects of changing acceleration. The second set of results investigate how the Dirac field can be confined to a cavity for quantum information purposes. By again considering Bogoliubov transformations, we thoroughly investigate how the entanglement shared between two cavities is affected by non-uniform motion. It is shown that different types of Dirac field states are more robust against motion than others. The final results look at using our second notion of localisation, Unruh- DeWitt detectors. We investigate how allowing for a "non-point-like" spatial profile of the Unruh-DeWitt detector affects how it interacts with a quantum field around it. By engineering suitable detector-field interactions, we use techniques from symplectic geometry to compute the dynamics of a quantum state beyond commonly used perturbation theory. There is also a conclusions chapter at the end of the thesis which summarises the results presented and suggestions of possible new directions of research in relativistic quantum information are made.