Precision Bounds for Characterising Quantum Measurements

TL;DR

This paper introduces a comprehensive framework for efficiently characterising quantum measurements, establishing fundamental limits and differences from state estimation, with practical validation for current quantum detector technologies.

Contribution

It develops a detector quantum Fisher information framework that simplifies detector estimation without needing optimal probe states, advancing quantum tomography methods.

Findings

Reveals fundamental limits to parameter extraction in quantum detectors.

Provides a robust, experimentally validated framework for detector estimation.

Connects detector analysis with state and process tomography in quantum information.

Abstract

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.