Related papers: Fisher Information inequalities and the Central Li…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the…
We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…
The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show…
It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramer-Rao bound (CRB), a popular tool to lower bound the…
Combining the ideas of quantum Fisher information and quantum renormalization group method, the Berezinskii-Kosterlitz-Thouless quantum phase transition of spin- 1/2 XXZ chain is investigated. Quantum Fisher informations of the whole N…
We make use of an entropic property to establish a convergence theorem (Main Theorem), which reveals that the conditional entropy measures the asymptotic Gaussianity. As an application, we establish the {\it entropic conditional central…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
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…
Starting with the relative entropy based on a previously proposed entropy function $S_q[p]=\int dx p(x)(-\ln p(x))^q$, we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
We present in this work variants of existing estimates for the Landau or Landau-Fermi-Dirac entropy dissipation, in terms of Fisher information, in the hard potential case. The specificity of those variants is that the entropy is never used…
We show how a central limit theorem for Poisson model random polygons implies a central limit theorem for uniform model random polygons. To prove this implication, it suffices to show that in the two models, the variables in question have…
Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is…
We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states…
We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…
Recent theoretical and experimental work has shown that the quantum Fisher information associated with estimating the separation between two optical point sources remains finite at small separations, effectively opening new routes to…
We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced…
This note reviews a recent contribution about the Fisher information for the space-homogeneous Boltzmann equation by L. Silvestre, C. Villani and the author (arXiv, 2024). This classical functional from information theory is shown to be…
In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear)…
The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…