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The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…
This paper considers the problem of state tracking with observation control for a particular class of dynamical systems. The system state evolution is described by a discrete-time, finite-state Markov chain, while the measurement process is…
Quantum synchronization has emerged as a crucial phenomenon in quantum nonlinear dynamics with potential applications in quantum information processing. Multiple measures for quantifying quantum synchronization exist. However, there is…
We study how the amount of correlation between observations collected by distinct sensors/learners affects data collection and collaboration strategies by analyzing Fisher information and the Cramer-Rao bound. In particular, we consider a…
Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…
A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…
The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian…
The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…
Basic general properties are considered for the Fisher-type information involving higher order derivatives. They are used to explore various properties of probability densities and to derive Stam-type inequalities.
Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system…
Choosing a suitable loss function is essential when learning by empirical risk minimisation. In many practical cases, the datasets used for training a classifier may contain incorrect labels, which prompts the interest for using loss…
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…
Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…
We consider the problem of distributed estimation, where local processors observe independent samples conditioned on a common random parameter of interest, map the observations to a finite number of bits, and send these bits to a remote…
We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…
New inequalities are proved for the variance of the Pitman estimators (minimum variance equivariant estimators) of \theta constructed from samples of fixed size from populations F(x-\theta). The inequalities are closely related to the…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
We consider a general stochastic input-output dynamical system with output evolving in time as the solution to a functional coefficients, It\^{o}'s stochastic differential equation, excited by an input process. This general class of…
By using the $q$-Gaussian distribution derived by the maximum entropy method for spatially-correlated $N$-unit nonextensive systems, we have calculated the generalized Fisher information matrix of $g_{\theta_n \theta_m}$ for $(\theta_1,…