Quantum technologies rest on a triad of states, processes and measurements, but the precision limits for characterising measurements have remained poorly understood. Detector calibration therefore lacked a suitable notion of optimality.

Our recent work introduced the detector quantum Fisher information (DQFI), a fundamental metric that sets the ultimate precision achievable in measurement calibration. An unknown measurement is probed with a known quantum state, and a parameter of the measurement is inferred from the output statistics. The optimal probe is the one that maximises the classical Fisher information of these statistics.

We developed an analytical solution for phase-insensitive detectors, including avalanche photodiodes and photon-number-resolving detectors, and an efficient semidefinite program for phase-sensitive measurements. The framework was demonstrated experimentally on an IBM quantum processor by estimating the dephasing strength of a qubit measurement.

This project will extend the DQFI framework to an open problem selected according to the student’s background and level. Possible directions include continuous-variable probes, such as displaced squeezed states for photodetector calibration; distinct forms of incompatibility in multi-parameter detector models; or error-correction strategies that may preserve Heisenberg scaling under realistic noise. The work may involve analytical quantum estimation theory, numerical optimisation, and/or experimental implementation.