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. 2018 Sep 24;8:14278. doi: 10.1038/s41598-018-32434-x

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© The Author(s) 2018

Open Access 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 http://creativecommons.org/licenses/by/4.0/.

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The figure shows the fidelity for the estimation of the power spectral density S(ω) as a function of the dephasing rate Γ. For each value of Γ, we choose the filter operation time such that the fidelity is maximized. This optimal time is obtained from a scan of different values of the filter operation time T both for the AS and FO protocol as in the example of Fig. 2. The optimal filter operation time depends on Γ and on the protocol, and was found to be in the range [5, 25] for the AS protocol and [2, 5] for the FO protocol.