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The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…

Quantum Physics · Physics 2021-03-15 Jianning Li , Haodi Liu , Zhihai Wang , Xuexi Yi

Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…

Information Theory · Computer Science 2023-11-27 Ori Aharon , Joseph Tabrikian

We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training and population loss. The bounds hold under the assumption…

Machine Learning · Computer Science 2024-02-22 Fredrik Hellström , Benjamin Guedj

A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…

Quantum Physics · Physics 2017-01-18 Luigi Seveso , Matteo A. C. Rossi , Matteo G. A. Paris

In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on…

Mathematical Physics · Physics 2013-01-18 J. -F. Bercher

In this lecture note, we show a general property of the Cramer-Rao bound (CRB) that quantifies the interdependencies between the parameters in a vector. The presented result is valid for more general models than the additive noise model and…

Statistics Theory · Mathematics 2015-05-07 Dave Zachariah , Petre Stoica

A common assumption in signal processing is that underlying data numerically conforms to a Gaussian distribution. It is commonly utilized in signal processing to describe unknown additive noise in a system and is often justified by citing…

Signal Processing · Electrical Eng. & Systems 2025-10-14 Jennie Couchman , Phillip Stanley-Marbell

We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…

Statistics Theory · Mathematics 2022-08-25 Worachet Bukaew , Sikarin Yoo-Kong

In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of…

Quantum Physics · Physics 2020-02-12 Xiao-Ming Lu , Zhihao Ma , Chengjie Zhang

The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…

Signal Processing · Electrical Eng. & Systems 2025-05-20 Shiraz Khan , Gregory S. Chirikjian

The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…

Quantum Physics · Physics 2018-09-26 Luigi Seveso , Matteo G. A. Paris

We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…

Information Theory · Computer Science 2015-06-04 Paul Tune

Advanced super-resolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to Cramer-Rao bound (CRB) has proved to be a powerful and…

This paper derives a general expression for the Cram\'er-Rao bound (CRB) of wireless localization algorithms using range measurements subject to bias corruption. Specifically, the a priori knowledge about which range measurements are…

Information Theory · Computer Science 2011-11-10 Tao Wang

Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their…

We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the…

Statistics Theory · Mathematics 2018-01-24 Victor Chernozhukov , Denis Chetverikov , Kengo Kato

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…

Quantum Physics · Physics 2023-07-27 M. Gessner , A. Smerzi

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…

Quantum Physics · Physics 2017-05-04 R. Yousefjani , S. Salimi , A. S. Khorashad

This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…

Machine Learning · Statistics 2018-01-01 Jian Du , Shaodan Ma , Yik-Chung Wu , Soummya Kar , José M. F. Moura

We compare the latest results from CMB experiments at scales around $l_e \sim 150$ over different parts of the sky to test the hypothesis that they are drawn from a Gaussian distribution, as is usually assumed. Using both the diagonal and…

Astrophysics · Physics 2009-10-30 E. Gaztanaga , P. Fosalba , E. Elizalde