Estimating imprecision lower bound in a neighbourhood of a known Cramér-Rao lower bound
Date
2024-09-20
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Abstract
The ultimate metrology limit, classical or quantum, for estimating an unknown parameter defining a distribution of measurement outcomes, is determined by the Cramér-Rao lower bound (CRLB). However, which distribution pertains to the measurement setup can itself fluctuate for running each trial of the experiment or even within one run, meaning that we are estimating the distribution parameter in the case that we have a distribution of distributions. Our aim is to estimate the imprecision CRLB for the parameter of a distribution but in a small neighbourhood of this distribution rather than precisely at this parameter. We determine this CRLB in a neighbourhood by calculating a Taylor expansion of the Fisher information for the distribution in a neighbourhood of its defining parameter, obtain the expression for the CRLB for each distribution in this neighbourhood and then calculate the average CRLB over this neighbourhood. We illustrate our result for the case of two-parameter estimation in SU(2) interferometry for which singularities of the CRLB arise, making this averaging not just illustrative but also needed to circumvent the singularity.
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Fisher information, Cramér-Rao lower bound, Mach–Zehnder interferometer, Singular matrices, Quantum metrology, Parameter estimation
Citation
Salimi Moghadam, M. (2024). Estimating imprecision lower bound in a neighbourhood of a known Cramér-Rao lower bound (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.