Diagnosing Imperfections in Quantum Sensors via Generalized Cramér-Rao Bounds

Cimini, Valeria; Genoni, Marco G.; Gianani, Ilaria; Spagnolo, Nicolò; Sciarrino, Fabio; Barbieri, Marco

doi:10.1103/physrevapplied.13.024048

Cited by 9 publications

(5 citation statements)

References 35 publications

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“…While much progress has been made for CV parameter estimation within the local paradigm, in particular, regarding the calculation of the quantum Fisher information (QFI) [6][7][8][9][11][12][13][14][15] and the associated optimal strategies achieving the CRB [24][25][26][27][28][29], CV parameter estimation in the Bayesian setting is much less explored. There, recent work has provided insight into Bayesian estimation with discrete [30] and CV systems using some specific probe states, including coherent states [16][17][18]31], N00N states [16,32], and single-photon states [33]. Determining efficient and practically realizable strategies for Bayesian estimation in quantum optical systems can thus be considered an important link in the development of quantum sensing technologies, which this paper aims to establish.…”

Section: Introductionmentioning

confidence: 99%

Bayesian parameter estimation using Gaussian states and measurements

Morelli

Usui

Agudelo

et al. 2021

Quantum Sci. Technol.

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Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramér–Rao bound (CRB) is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable (CV) quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.

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Section: Introductionmentioning

confidence: 99%

Bayesian parameter estimation using Gaussian states and measurements

Morelli

Usui

Agudelo

et al. 2021

Quantum Sci. Technol.

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“…that corresponds to the mean value of the parameter over the posterior distribution. Also other moments, such as the third moment, of such distribution can be informative on the estimation, especially to detect possible biases 188 . The phase shift φ estimated inside an interferometer is a circular parameter, where φ = φ + 2kπ with k ∈ Z.…”

Section: Estimatorsmentioning

confidence: 99%

Photonic Quantum Metrology

Polino¹,

Valeri²,

Spagnolo³

et al. 2020

Preprint

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Quantum Metrology is one of the most promising application of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here we review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to phase estimation. We describe the current state of the art in the field in terms of platforms and quantum resources. Furthermore, we present the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time. We conclude by discussing the current experimental and theoretical challenges, and the open questions towards implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise.

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“…Although current efforts to improve the sensitivity and utility of quantum sensors is focused on the use of non-classical states [1], the development of sophisticated data analysis techniques to extract information encoded in complex quantum states is also an important aspect of this effort. High quality device calibration is essential for such efforts [28,[32][33][34][35][36][37][38][39]. In particular, the calibration of a generic quantum sensors through the lens of supervised machine learning offers interesting possibilities [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Frequentist Parameter Estimation with Supervised Learning

Nolan¹,

Pezzé²,

Smerzi³

2021

Preprint

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Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machinelearned point estimate of an unknown parameter. Although the analysis is neccessarily frequentistrelying on repeated esitmates to build up statistics -we clarify that this machine-learned estimator converges to the Bayesian maximum a-posterori estimator (subject to some regularity conditions). When the number of training measurements are large, this is identical to the well-known maximumlikelihood estimator (MLE), and using this fact, we argue that the Cramér-Rao sensitivity bound applies to the mean-square error cost function and can therefore be used to select optimal model and training parameters. We show that the machine-learned estimator inherits the desirable asymptotic properties of the MLE, up to a limit imposed by the resolution of the training grid. Furthermore, we investigate the role of quantum noise the training process, and show that this noise imposes a fundamental limit on number of grid points. This manuscript paves the way for machine-learning to assist the calibration of quantum sensors, thereby allowing maximum-likelihood inference to play a more prominent role in the design and operation of the next generation of ultra-precise sensors.

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Diagnosing Imperfections in Quantum Sensors via Generalized Cramér-Rao Bounds

Cited by 9 publications

References 35 publications

Bayesian parameter estimation using Gaussian states and measurements

Bayesian parameter estimation using Gaussian states and measurements

Photonic Quantum Metrology

Frequentist Parameter Estimation with Supervised Learning

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