Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound
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. Wh...
| Main Authors: | , , |
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| Format: | Article |
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IOP Publishing
2017
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| Online Access: | https://eprints.nottingham.ac.uk/48801/ |
| _version_ | 1848797850826178560 |
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| author | Rubio Jiménez, Jesús Knott, Paul Dunningham, Jacob A. |
| author_facet | Rubio Jiménez, Jesús Knott, Paul Dunningham, Jacob A. |
| author_sort | Rubio Jiménez, Jesús |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:10:26Z |
| format | Article |
| id | nottingham-48801 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:10:26Z |
| publishDate | 2017 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-488012020-05-04T19:22:44Z https://eprints.nottingham.ac.uk/48801/ Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound Rubio Jiménez, Jesús Knott, Paul Dunningham, Jacob A. 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. IOP Publishing 2017-12-15 Article PeerReviewed Rubio Jiménez, Jesús, Knott, Paul and Dunningham, Jacob A. (2017) Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound. Journal of Physics Communications . ISSN 2399-6528 (In Press) http://iopscience.iop.org/article/10.1088/2399-6528/aaa234 doi:10.1088/2399-6528/aaa234 doi:10.1088/2399-6528/aaa234 |
| spellingShingle | Rubio Jiménez, Jesús Knott, Paul Dunningham, Jacob A. Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound |
| title | Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound |
| title_full | Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound |
| title_fullStr | Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound |
| title_full_unstemmed | Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound |
| title_short | Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound |
| title_sort | non-asymptotic analysis of quantum metrology protocols beyond the cramér-rao bound |
| url | https://eprints.nottingham.ac.uk/48801/ https://eprints.nottingham.ac.uk/48801/ https://eprints.nottingham.ac.uk/48801/ |