Encoding parameters by measurement: Forgetting can be better in quantum metrology

Abstract:We introduce quantum parameter estimation with the encoding being via a quantum measurement. We quantify the precision for estimating parameters characterizing a general two-outcome qubit measurement, considering two cases: when the outcomes of the encoding measurement are recorded and when the same are ignored. We find that in a large variety of such estimation scenarios, forgetting the outcomes yields higher precision. We derive a necessary criterion under which remembering the measurement outcomes provides better precision in comparison to the outcome-forgotten strategy. Furthermore, we establish a necessary and sufficient criterion for the simultaneous estimation of multiple parameters encoded by an arbitrary quantum process, including those involving measurements, using qubit probes, and find when the quantum Cramér$-$Rao bound is valid and achievable. For simultaneous estimation of two parameters characterizing the measurement, we find that the achievable quantum Cramér$-$Rao bound can be a valid precision bound only when the measurement direction depends on the parameters of interest.

arXiv:2512.10541 [quant-ph]

(or arXiv:2512.10541v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.10541 Focus to learn more arXiv-issued DOI via DataCite

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