Related papers: Fisher Information of Scale
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…
The problem how to approximately determine the absolute value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric…
This paper deals with the Fisher-consistency, weak continuity and differentiability of estimating functionals corresponding to a class of both linear and nonlinear regression high breakdown M estimates, which includes S and MM estimates. A…
We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…
The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…
The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model…
We derive upper bounds on the quantum Fisher information in interferometry with $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence of arbitrarily correlated Gaussian dephasing including independent and collective…
The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions…
Many real-world tasks include some kind of parameter estimation, i.e., determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic…
In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher…
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
The Fisher information matrix provides a way to measure the amount of information given observed data based on parameters of interest. Many applications of the FIM exist in statistical modeling, system identification, and parameter…
We show that the variance is its own concave roof. For rank-2 density matrices and operators with zero diagonal elements in the eigenbasis of the density matrix, we prove analytically that the quantum Fisher information is four times the…
Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an…
We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…
We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated…
Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…
We consider the behaviour of the Fisher information of scaled sums of independent and identically distributed random variables in the Central Limit Theorem regime. We show how this behaviour can be related to the second-largest non-trivial…
A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-L\^e-Schwachh\"ofer. We introduce a…
In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square…