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Benchmarking Bayesian quantum estimation
Quantum Physics · Submitted 26 Jan 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities.
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The abstract, sentence by sentence
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The quest for precision in parameter estimation is a fundamental task in different scientific areas. | background 1.00 | 0.03 | 0.01 | asserted 1.00 |
| s1 | The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. | background 1.00 | 0.06 | 0.02 | asserted 0.99 |
| s2 | Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. | background 1.00 | 0.06 | 0.03 | asserted 1.00 |
| s3 | However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. | background 0.64 | 0.07 | 0.02 | asserted 0.99 |
| s4 | Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. | background 0.60 | 0.05 | 0.02 | hedged possibility 0.70 |
| s5 | This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. | contribution 1.00 | 0.67 | 0.09 | asserted 0.95 |
| s6 | By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. | result 0.87 | 0.90 | 0.77 | asserted 0.98 |
| s7 | These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework. | interpretation 0.97 | 0.74 | 0.31 | asserted 0.96 |
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The paper
Original abstract
The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.
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References
How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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Dating back to the early days of the field [ref] , it is nowadays being increasingly applied to a wide range of multiparameter sensing experiments involving both photons [ref] and atoms [ref] .
Measurement incompatibility in Bayesian multiparameter quantum estimation · Introduction · 0.88
What it cites · 3 sentences without a confident label
Uses the method or tool of 1 paper
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This discretization was conducted in accordance with SMC, also known as the particle filtering method [ref] , used in recent multiparameter estimation experiments [ref] .
Optimizing quantum-enhanced Bayesian multiparameter estimation of phase and noise in practical sensors · Single parameter case · 0.92
Cites as background 3 papers
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Such a bound sets a lower fundamental limit on the variance (the covariance matrix $Σ(ϕ⃗)$ in the multiparameter case) of unbiased estimators: [equation] where $N$ represents the number of employed independent probes, $F(ϕ)$ and $𝔽(ϕ⃗)$ are the Fisher Information and the Fisher Information matrix respectively [ref] .
Fisher information susceptibility for multiparameter quantum estimation · Figures of merit in estimation protocols · 0.94
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Among the others, it includes machine learning-based algorithms [ref] , variational techniques [ref] , Bayesian updates based on minimizing the variance of the posterior [ref] , particle swarm optimization [ref] , genetic algorithms [ref] , or differential evolution [ref] .
Optimizing quantum-enhanced Bayesian multiparameter estimation of phase and noise in practical sensors · Multiparameter case · 0.81
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Among the others, it includes machine learning-based algorithms [ref] , variational techniques [ref] , Bayesian updates based on minimizing the variance of the posterior [ref] , particle swarm optimization [ref] , genetic algorithms [ref] , or differential evolution [ref] .
Variational quantum algorithm for experimental photonic multiparameter estimation · Multiparameter case · 0.81
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