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| Journal Article | FZJ-2025-05656 |
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2025
Inst.
Woodbury, NY
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Please use a persistent id in citations: doi:10.1103/PhysRevA.111.042218 doi:10.34734/FZJ-2025-05656
Abstract: The formalism of quantum estimation theory with a specific focus on classical data postprocessing is appliedto a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentistapproaches to estimate the unknown transition frequency. In the frequentist approach, we have shown thatonly reducing the distance between the classical and the quantum Fisher information does not necessarilymean that the estimators as functions of the data deliver an estimate with desirable accuracy, as the classicalFisher information takes small values. We have proposed and investigated a cost function to account for themaximization of the classical Fisher information and the minimization of the aforementioned distance. Dueto the nonlinearity of the probability mass function of the data on the transition frequency, the minimumvariance unbiased estimator may not exist. The maximum likelihood and the maximum a posteriori estimatorsoften result in ambiguous estimates, which in certain cases can be made unambiguous upon changing theparameters of the external field. It is demonstrated that the minimum mean-square error estimator of the Bayesianstatistics provides unambiguous estimates. In the Bayesian approach, we have also investigated the effects ofnoninformative and informative priors on the Bayesian estimates, including a uniform prior, Jeffrey’s prior, anda Gaussian prior.
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