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

Rubio Jiménez, Jesús; Knott, Paul; Dunningham, Jacob A.


Jesús Rubio Jiménez

Jacob A. Dunningham


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.


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, doi: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 Aug 16, 2018
Journal Journal of Physics Communications
Electronic ISSN 2399-6528
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 2
Article Number 015027
Public URL
Publisher URL
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf


manuscript_final_version_JPCO_100307.R1.pdf (775 Kb)

AM - Accepted Manuscript

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