Ultimate estimation limits in electron-positron interactions

Project ID: 2228cd1412 (You will need this ID for your application)

UCL Lead department: Physics and Astronomy

Project Summary:

PET scanning technologies have revolutionised medical imaging over the past 50 years and keep evolving at a great pace, as shown by the recent introduction of total-body scans offering unprecedented diagnostics of metabolic molecular processes. The spatial precision of PET techniques hinges on the angular resolution of photon pairs emitted from electron-positron annihilations. It would therefore be of great importance to establish the fundamental limits to angular resolution in QED processes involving electron-positron annihilation. This project aims at determining such limits by applying recently developed techniques from quantum information theory to quantum electrodynamics.

In particular, the student will consider first electron-positron scattering at tree-level and determine the resulting, momentum-filtered helicity density matrix, which will depend on the scattering angle. Hence, the quantum Fisher information associated with such an angle will be determined and, with it, the ultimate, optimal measurement associated with the optimal determination of such an angle. As a byproduct, this will give strong indications as to the ultimate resolution PET scans may ever achieve. The project will then be further developed by considering higher-order, loop effects, numerically and through renormalisation group techniques. Also, the possible effects of positronium formation and annihilation will be considered, by employing bound-state QED.

Practical implications of the project’s findings will be pursued and exploited wherever possible, in direct collaboration with the experimental team led by the second supervisor, who has a longstanding experience in studying positronium formation and detection.

This project caters to candidates with a strong penchant for theoretical and mathematical physics, as well as notable numerical skills. The student would in fact have to develop a substantial familiarity with quantum field theory, as well as with quantum information theory.