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Quantum metrology with imperfect measurements

Len, Yink Loong and Gefen, Tuvia and Retzker, Alex and Kołodyński, Jan (2022) Quantum metrology with imperfect measurements. Nature Communications, 13 . Art. No. 6971. ISSN 2041-1723. PMCID PMC9666656. doi:10.1038/s41467-022-33563-8.

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The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections—with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.

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URLURL TypeDescription CentralArticle
Len, Yink Loong0000-0003-4810-3917
Gefen, Tuvia0000-0002-3235-4917
Retzker, Alex0000-0002-7291-7120
Kołodyński, Jan0000-0001-8211-0016
Additional Information:This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit The authors are thankful to Spyridon Michalakis and Michał Oszmaniec for fruitful discussions. Y.L.L. & J.K. acknowledge financial support from the Foundation for Polish Science within the “Quantum Optical Technologies” project carried out within the International Research Agendas programme co-financed by the European Union under the European Regional Development Fund. T.G. acknowledges the support of the Israel Council for Higher Education Quantum Science and Technology Scholarship. Contributions. All Y.L.L., T.G., and J.K. contributed extensively to preparing the manuscript with the leading input from Y.L.L. They all contributed to developing the ideas, performing the calculations, and preparing the results, with J.K. also supervising the work. T.G. and A.R. had conceived the original idea and motivation, providing the expertise on NV-centre-based experiments. Data availability. All data relevant to this study are available from the corresponding authors upon request. Code availability. The code used for simulations is available from the corresponding authors upon request.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Foundation for Polish ScienceUNSPECIFIED
European Regional Development FundUNSPECIFIED
Israel Council for Higher EducationUNSPECIFIED
PubMed Central ID:PMC9666656
Record Number:CaltechAUTHORS:20221205-666301600.17
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118241
Deposited By: Research Services Depository
Deposited On:06 Jan 2023 22:07
Last Modified:06 Jan 2023 22:07

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