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To any parametric family of states of a finite level quantum system we associate a space of Fisher maps and introduce the natural notions of Cram\'er-Rao-Bhattacharya tensor and Fisher information form. This leads us to an abstract…

Probability · Mathematics 2009-07-14 K. R. Parthasarathy

The electronic local density of states of solids, if normalized correctly, represents the probability density that the electron at a specific position has a particular energy. Because this probability density can vary in space in disordered…

Strongly Correlated Electrons · Physics 2025-05-30 Lucas A. Oliveira , Wei Chen

We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A…

Quantum Physics · Physics 2018-08-22 Geza Toth

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 statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cram\'er-Rao inequality is…

Quantum Physics · Physics 2023-01-18 Nour-Eddine Abouelkhir , Hanane EL Hadfi , Abdallah Slaoui , Rachid Ahl Laamara

The efficient sensing of weak environmental perturbations via special degeneracies called exceptional points in non-Hermitian systems has gained enormous traction in the last few decades. However, in contrast to the extensive literature on…

Quantum Physics · Physics 2022-03-02 J. Wang , D. Mukhopadhyay , G. S. Agarwal

The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…

Quantum Physics · Physics 2018-03-30 Matthias M. Müller , Stefano Gherardini , Augusto Smerzi , Filippo Caruso

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 places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given…

Quantum Physics · Physics 2013-02-22 Sixia Yu

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…

Quantum Physics · Physics 2016-05-11 Nan Li , Christopher Ferrie , Jonathan A. Gross , Amir Kalev , Carlton M. Caves

We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…

Statistical Mechanics · Physics 2020-07-01 Sosuke Ito , Andreas Dechant

A closed-form expression for Wigner-Yanase skew information in mixed-state quantum systems is derived. It is shown that limit values of the mixing coefficients exist such that Wigner-Yanase information is equal to Helstrom information. The…

Statistics Theory · Mathematics 2011-04-22 Alessandra Luati

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

We present several inequalities related to the Robertson-Schr\"odinger uncertainty relation. In all these inequalities, we consider a decomposition of the density matrix into a mixture of states, and use the fact that the…

Quantum Physics · Physics 2024-01-23 Géza Tóth , Florian Fröwis

Localization of a non-cooperative target with binary detectors is considered. A general expression for the Fisher information for estimation of target location and power is developed. This general expression is then used to derive…

Information Theory · Computer Science 2014-07-29 Arian Shoari , Alireza Seyedi

In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the…

Information Theory · Computer Science 2013-05-28 Jean-François Bercher

This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of…

Statistics Theory · Mathematics 2026-04-02 Telmo Pérez-Izquierdo

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

Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…

Classical Physics · Physics 2023-10-06 Mohamed Sahbani , Swetamber Das , Jason R. Green

In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for…

Mathematical Physics · Physics 2019-09-04 Marcelo Losada , Ignacio S. Gomez , Federico Holik