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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

Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…

Quantum Physics · Physics 2018-01-31 Jesús Rubio , Paul Knott , Jacob Dunningham

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed…

Quantum Physics · Physics 2020-03-27 Jing Liu , Haidong Yuan , Xiao-Ming Lu , Xiaoguang Wang

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup,…

Statistics Theory · Mathematics 2024-09-10 Florent Bouchard , Alexandre Renaux , Guillaume Ginolhac , Arnaud Breloy

In information geometry, statistical models are considered as differentiable manifolds, where each probability distribution represents a unique point on the manifold. A Riemannian metric can be systematically obtained from a divergence…

Statistics Theory · Mathematics 2025-07-29 Satyajit Dhadumia , M. Ashok Kumar

The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…

Statistics Theory · Mathematics 2016-11-24 Dave Zachariah , Petre Stoica

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

The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…

Machine Learning · Statistics 2024-09-09 Evan Scope Crafts , Xianyang Zhang , Bo Zhao

We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…

Quantum Physics · Physics 2017-06-08 Marco G. Genoni

The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…

Methodology · Statistics 2023-02-07 Maud Delattre , Estelle Kuhn

In this paper, the Cram\'{e}r-Rao Bounds (CRB) for the simultaneous estimation of power system electromechanical modes and forced oscillations (FO) are derived. Two cases are considered; in the first case only the steady-state response to…

Signal Processing · Electrical Eng. & Systems 2025-11-21 Luke Dosiek

The Fisher information matrix (FIM) is a fundamental quantity to represent the characteristics of a stochastic model, including deep neural networks (DNNs). The present study reveals novel statistics of FIM that are universal among a wide…

Machine Learning · Statistics 2019-10-10 Ryo Karakida , Shotaro Akaho , Shun-ichi Amari

The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we…

Information Theory · Computer Science 2025-01-08 Frank Nielsen

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

In location estimation, we are given $n$ samples from a known distribution $f$ shifted by an unknown translation $\lambda$, and want to estimate $\lambda$ as precisely as possible. Asymptotically, the maximum likelihood estimate achieves…

Statistics Theory · Mathematics 2023-02-07 Shivam Gupta , Jasper C. H. Lee , Eric Price

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…

Quantum Physics · Physics 2009-11-07 Denes Petz

In this paper, we derive the Cramer-Rao bound (CRB) for joint target position and velocity estimation using an active or passive distributed radar network under more general, and practically occurring, conditions than assumed in previous…

Statistics Theory · Mathematics 2016-04-20 Qian He , Jianbin Hu , Rick S. Blum , Yonggang Wu

RF fingerprinting authenticates satellite transmitters by exploiting hardware-specific signal impairments, yet existing methods operate without theoretical performance guarantees. We derive the Fisher information matrix (FIM) for joint…

Signal Processing · Electrical Eng. & Systems 2026-04-01 Haofan Dong , Ozgur B. Akan

Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to…

Quantum Physics · Physics 2024-02-12 Christoph Hotter , Helmut Ritsch , Karol Gietka

Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces…

Machine Learning · Statistics 2026-01-08 Bing Cheng , Howell Tong