Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Letters A

The influence of non-Gaussian noise on the accuracy of parameter estimation

Xuelian Li, Jungang Li, Yuanmei Wang

Published Nov 2, 2016• 6 citations
Publisher
DOI
10.1016/j.physleta.2016.10.050

Related papers

The influence of non-Gaussian noise on weak values

Fangyuan Ma, Jungang Li, Jian Zou

Physics Letters A•Nov 19, 2020•4 citations

Influence of parameter prior information on effect of colored noise in Bayesian frequency estimation

Di Yang, Wang Yuan-Mei, Li Jun-Gang

Parameter estimation, which undertakes one of the vital missions in quantum metrology, has attracted a lot of attention in recent years. A large number of investigations on the frequency estimation have been carried out. Most of them are based on Cramér-Rao bound estimation approach in which almost perfect knowledge of the parameter to be estimated is given. In reality, however, one has inadequate prior knowledge about the parameter to be estimated. Then the Bayesian estimation approach in which we can perform the estimation even if we only have partial prior information about the parameter would be an ideal choice. Prior information about the parameter can play a significant role in Bayesian statistical inference. So it is interesting to know how the prior knowledge affects the estimation accuracy in the estimation process. In the solid-state realization of probe system, material-specific fluctuations typically lead to the major contribution to the intrinsic noise. Then it is interesting to study the effects of colored noise on the quantum parameter estimation. In this work, we study the inhibitory effects of prior probability distribution of the parameter to be estimated on the effects of colored noise under the framework of Bayesian parameter estimation theory. In particular, we estimate the intensity of a magnetic field by adopting a spin-1/2 system which is influenced by the colored noise with 1/fα spectrum. To evaluate the accuracy of estimation, we obtain the Bayes cost analytically which can be applied to the noisy channels. We mainly focus on the inhibitory effect of prior probability distribution of measured parameter on the non-Gaussianity of noise. We find that for the case of broad prior frequency distribution, the influence of non-Gaussianity on the estimation is very weak. While for the case of narrow prior frequency distribution, the influence of non-Gaussianity on the estimation is strong. That means that in the Bayesian approach, when we have enough prior information about the frequency, the non-Gaussianity can conduce to the improvement of the accuracy of the estimation of the frequency. When we lose the prior information, we also lose the improvement of the accuracy from the non-Gaussianity. The uncertainty of the prior information tends to eliminate the effects of the non-Gaussianity of the noise.

Acta Physica Sinica•Jan 1, 2018•0 citations

Ultimate precision of joint parameter estimation under noisy Gaussian environment

Bakmou Lahcen, Mohammed Daoud A

Physics Letters A•Jan 19, 2022•8 citations

Estimation of Variance and Skewness of non-Gaussian zero mean white noise from measurements of the atomic transition probabilities

Kapil Prajapati, Harish Parthasarthy

Estimation of noise parameters is always an important and tedious task when the system under consideration is of the order of atomic level. The majority of estimation algorithms available in the literature assume that the additive noise has a Gaussian distribution. Though it is good model for thermal noise, but in the real world, noise experienced is due to a variety of man-made sources, which deviates from the Gaussian way and is non-Gaussian in nature. Though there are other methods to estimate the parameters of a random non-Gaussian process, for e.g. - Maximum Likelihood Estimator (MLE). In order to construct the MLE of σ2and γ based on quantum measurement would involve constructing the joint pdf of the samples of complex wave function at discrete times. This would be a highly nonlinear function of σ2and γ. The optimization would involve computationally heavy search algorithms. Moments matching is simpler though sub optimal and hence, we have chosen this. In this paper, we proposed a new method to estimate the parameters of non-Gaussian random process based on the higher order statistics (spectra) analysis and quantum measurement which involve the measurement of atomic transition probabilities. Simulated results and comparison between the theoretical values of Variance (finite) and Skewness (non-zero triple moment) have been presented here.

International Conference on Signal Propagation and Computer Technology (ICSPCT)•Jul 1, 2014•0 citations

Statistical Models for Noisy Measurements

Jochen Szangolies

Springer eBooks•Jan 1, 2015•0 citations

Effect of prior information on noisy Bayesian frequency estimation

Jungang Li, Yuanmei Wang, Di Yang +1 more

Quantum frequency estimation under general noise is investigated in the Bayesian parameter estimation approach. To evaluate the accuracy of estimation, the Bayes cost is obtained analytically which can be applied to the common noisy channels, such as the phase-damping channel, the amplitude-damping channel, and the depolarizing channel. The Bayes cost formula clearly shows that the prior information imposes a restriction upon the effect of noise in the estimation process. Three examples of frequency estimations are provided to illustrate the roles of prior probability in the estimation process. It is found that, due to the restriction of prior information on the noise, the estimation accuracy is less sensitive to the noise in the Bayesian approach than that in the Cram\'er-Rao bound approach. More prior information can help us to use the non-Gaussianity of the noise channel to improve the estimation accuracy in the phase-damping channel.

Physical Review A•Nov 27, 2017•4 citations
Parameter estimation, which undertakes one of the vital missions in quantum metrology, has attracted a lot of attention in recent years. A large number of investigations on the frequency estimation have been carried out. Most of them are based on Cramér-Rao bound estimation approach in which almost perfect knowledge of the parameter to be estimated is given. In reality, however, one has inadequate prior knowledge about the parameter to be estimated. Then the Bayesian estimation approach in which we can perform the estimation even if we only have partial prior information about the parameter would be an ideal choice. Prior information about the parameter can play a significant role in Bayesian statistical inference. So it is interesting to know how the prior knowledge affects the estimation accuracy in the estimation process. In the solid-state realization of probe system, material-specific fluctuations typically lead to the major contribution to the intrinsic noise. Then it is interesting to study the effects of colored noise on the quantum parameter estimation. In this work, we study the inhibitory effects of prior probability distribution of the parameter to be estimated on the effects of colored noise under the framework of Bayesian parameter estimation theory. In particular, we estimate the intensity of a magnetic field by adopting a spin-1/2 system which is influenced by the colored noise with 1/fα spectrum. To evaluate the accuracy of estimation, we obtain the Bayes cost analytically which can be applied to the noisy channels. We mainly focus on the inhibitory effect of prior probability distribution of measured parameter on the non-Gaussianity of noise. We find that for the case of broad prior frequency distribution, the influence of non-Gaussianity on the estimation is very weak. While for the case of narrow prior frequency distribution, the influence of non-Gaussianity on the estimation is strong. That means that in the Bayesian approach, when we have enough prior information about the frequency, the non-Gaussianity can conduce to the improvement of the accuracy of the estimation of the frequency. When we lose the prior information, we also lose the improvement of the accuracy from the non-Gaussianity. The uncertainty of the prior information tends to eliminate the effects of the non-Gaussianity of the noise.
Estimation of noise parameters is always an important and tedious task when the system under consideration is of the order of atomic level. The majority of estimation algorithms available in the literature assume that the additive noise has a Gaussian distribution. Though it is good model for thermal noise, but in the real world, noise experienced is due to a variety of man-made sources, which deviates from the Gaussian way and is non-Gaussian in nature. Though there are other methods to estimate the parameters of a random non-Gaussian process, for e.g. - Maximum Likelihood Estimator (MLE). In order to construct the MLE of σ2and γ based on quantum measurement would involve constructing the joint pdf of the samples of complex wave function at discrete times. This would be a highly nonlinear function of σ2and γ. The optimization would involve computationally heavy search algorithms. Moments matching is simpler though sub optimal and hence, we have chosen this. In this paper, we proposed a new method to estimate the parameters of non-Gaussian random process based on the higher order statistics (spectra) analysis and quantum measurement which involve the measurement of atomic transition probabilities. Simulated results and comparison between the theoretical values of Variance (finite) and Skewness (non-zero triple moment) have been presented here.
Quantum frequency estimation under general noise is investigated in the Bayesian parameter estimation approach. To evaluate the accuracy of estimation, the Bayes cost is obtained analytically which can be applied to the common noisy channels, such as the phase-damping channel, the amplitude-damping channel, and the depolarizing channel. The Bayes cost formula clearly shows that the prior information imposes a restriction upon the effect of noise in the estimation process. Three examples of frequency estimations are provided to illustrate the roles of prior probability in the estimation process. It is found that, due to the restriction of prior information on the noise, the estimation accuracy is less sensitive to the noise in the Bayesian approach than that in the Cram\'er-Rao bound approach. More prior information can help us to use the non-Gaussianity of the noise channel to improve the estimation accuracy in the phase-damping channel.