Role of the filter functions in noise spectroscopy

Year: 2019

Authors: Dalla Pozza Nicola; Gherardini Stefano; Mueller Matthias M.; Caruso Filippo

Autors Affiliation: Dept. of Physics and Astronomy & LENS, University of Florence, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; Dept. of Physics and Astronomy & LENS, University of Florence, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; Forschungszentrum Julich, Peter Grunberg Inst Quantum Control PGI 8, D-52425 Julich, Germany

Abstract: The success of quantum noise sensing methods depends on the optimal interplay between properly designed control pulses and statistically informative measurement data on a specific quantum-probe observable. To enhance the information content of the data and reduce as much as possible the number of measurements on the probe, the filter orthogonalization method has been recently introduced. The latter is able to transform the control filter functions on an orthogonal basis allowing for the optimal reconstruction of the noise power spectral density. In this paper, we formalize this method within the standard formalism of minimum mean squared error estimation and we show the equivalence between the solutions of the two approaches. Then, we introduce a nonnegative least squares formulation that ensures the nonnegativeness of the estimated noise spectral density. Moreover, we also propose a novel protocol for the design in the frequency domain of the set of filter functions. The frequency-designed filter functions and the nonnegative least squares reconstruction are numerically tested on noise spectra with multiple components and as a function of the estimation parameters.

Journal/Review: INTERNATIONAL JOURNAL OF QUANTUM INFORMATION

Volume: 17 (8)      Pages from: 1941008-1  to: 1941008-16

More Information: N.D.P., S.G. and F.C. were financially supported by Fondazione CR Firenze, projects Q-BIOSCAN and Quantum-AI, by PATHOS EU H2020 FET-OPEN grant no. 828946, and by the University of Florence grant Q-CODYCES.
KeyWords: Quantum sensing, mean squared error estimation, noise spectroscopy
DOI: 10.1142/S0219749919410089

Citations: 1
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