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arXiv:2512.20091 · Nature Communications

Precision Bounds for Characterising Quantum Measurements

Aritra Das, Simon K. Yung, Lorcan O. Conlon, Ozlem Erkilic, Angus Walsh, Yong-Su Kim, Ping K. Lam, Syed M. Assad, Jie Zhao

quant-phphysics.ins-detphysics.opticsSubmitted Dec 23, 2025• Announced Dec 24, 2025• 1 citation
v1 · Dec 23, 2025v2 · Jan 22, 2026
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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 \emph{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.

Journal reference
Nat. Commun. (2026)
DOI
10.1038/s41467-026-68529-7
Comments
Accepted in Nat. Comms. (2025), presented at AIP (2025); 9 + 4 + 30 pages (main + methods + supplemental), 4 + 11 figures (main + supplemental)

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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 \emph{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.
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Abstract Quantum mechanics establishes the ultimate limit to the scaling of the precision on any parameter, by identifying optimal probe states and measurements. While this paradigm is, at least in principle, adequate for the metrology of quantum channels involving the estimation of phase and loss parameters, we show that estimating the loss parameters associated with a quantum channel and a realistic quantum detector are fundamentally different. While Fock states are provably optimal for the former, we identify a crossover in the nature of the optimal probe state for estimating detector imperfections as a function of the loss parameter using Fisher information as a benchmark. We provide theoretical results for on-off and homodyne detectors, the most widely used detectors in quantum photonics technologies, when using Fock states and coherent states as probes.