Precision bounds for characterising quantum measurements

Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this asymmetry by introducing a comprehensive framework for efficient detector estimation that reveals the fundamental limits to extractable parameter information and errors arising in detector analysis - the detector quantum Fisher information. Our development eliminates the need to optimise for the best probe state, while highlighting aspects of detector analysis that fundamentally differ from quantum state estimation. Through proofs, examples and experimental validation, we demonstrate the relevance and robustness of our proposal for current quantum detector technologies. By formalising a dual perspective to state estimation, our framework completes and connects the triad of efficient state, process, and detector tomography, advancing quantum information theory with broader implications for emerging technologies reliant on precisely calibrated measurements. In this work, the authors propose and experimentally test a framework to analyse the fundamental limits of quantum detector tomography, i.e., the limits to extractable information from probing unknown quantum measurements. They introduce the detector quantum Fisher information, which physically connects measurement structure to quantum advantage, complementing previously known state and channel metrics.