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Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound

Rubio Jim�nez, Jes�s; Knott, Paul; Dunningham, Jacob A.

Authors

Jes�s Rubio Jim�nez

Paul Knott

Jacob A. Dunningham



Abstract

Many results in the quantum metrology literature use the Cramér-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools, and these limitations are sometimes not taken into account. While a strategy that utilises this method can considerably simplify the problem and is valid asymptotically, to have a rigorous and fair comparison we need to adopt a more general approach. In this work we use a methodology based on Bayesian inference to understand what happens when the Cramér-Rao bound is not valid. In particular we quantify the impact of these restrictions on the overall performance of a wide range of schemes including those commonly employed for the estimation of optical phases. We calculate the number of observations and the minimum prior knowledge that are needed such that the Cramér-Rao bound is a valid approximation. Since these requirements are state-dependent, the usual conclusions that can be drawn from the standard methods do not always hold when the analysis is more carefully performed. These results have important implications for the analysis of theory and experiments in quantum metrology.

Citation

Rubio Jiménez, J., Knott, P., & Dunningham, J. A. (2018). Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound. Journal of Physics Communications, 2, Article 015027. https://doi.org/10.1088/2399-6528/aaa234

Journal Article Type Article
Acceptance Date Dec 15, 2017
Online Publication Date Jan 29, 2018
Publication Date Jan 29, 2018
Deposit Date Dec 19, 2017
Publicly Available Date Mar 28, 2024
Journal Journal of Physics Communications
Electronic ISSN 2399-6528
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 2
Article Number 015027
DOI https://doi.org/10.1088/2399-6528/aaa234
Public URL https://nottingham-repository.worktribe.com/output/900226
Publisher URL http://iopscience.iop.org/article/10.1088/2399-6528/aaa234

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