About the project
Quantum measurements often produce sparse, noisy observations from underlying sources or fields. This project develops mathematical methods for quantum measurement and sensing using random point sources, point processes and random measures, asking what source information can be recovered from realistic measurements and how noise and limited resolution affect that recovery.
Quantum measurements often provide indirect observations of an underlying source or field. Photon detections, interferometric measurements and spatial intensity data may be sparse, noisy and resolution limited, making recovery of the underlying physical structure an inverse problem.
This project will develop mathematical methods for quantum measurement and sensing based on random point sources, point processes and random measures. It will investigate how source configurations and their statistical properties are transformed by measurement, which features remain identifiable, and how uncertainty, correlations and non-Gaussian structure appear in observable data. Particular attention will be given to ambiguity, resolution, detector noise and restricted observation, leading to quantitative limits on source recovery, estimation and discrimination.
The project will use examples from quantum optics and quantum sensing, including photon counting, imaging and interferometric measurement, while remaining primarily mathematical and computational. It builds on Clark’s Random Point Sources: A Mathematical Theory of Point-Source Recovery (Springer, 2026), together with Field Theory for Point Processes (Birkhäuser) and Information and Inference for Point Processes (Springer).
The intended outcome is a rigorous theory of inverse problems for stochastic point sources under quantum measurement, with potential applications to quantum sensing, imaging, photodetection and measurement design.