Related papers: Fisher Information inequalities and the Central Li…
Fisher information is a measure of the best precision with which a parameter can be estimated from statistical data. It can also be defined for a continuous random variable without reference to any parameters, in which case it has a…
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…
For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three…
Point estimators may not exist, need not be unique, and their distributions are not parameter invariant. Generalized estimators provide distributions that are parameter invariant, unique, and exist when point estimates do not. Comparing…
We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
The dynamics of relative entropy and $l_{1}$-norm of coherence, as well as, the Wigner-Yanase-skew and quantum Fisher information are studied for a time-dependent coupled XY spin chain in presence of a time-dependent transverse magnetic…
The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…
The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
Parameter degeneracy in blazar spectral energy distributions (SEDs) is known but rarely quantified. This paper introduces a Fisher Information approach to determine theoretical limits to information extraction in the context of one-zone…
This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-known that the corresponding estimates satisfy a central…
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
Precision measurements with quantum systems rely on our ability to trace the differences between experimental signals to variations in unknown physical parameters. In this Letter we derive the Fisher information and the ensuing Cramer-Rao…
Fisher-information inequalities have recently been used as operational witnesses of nonclassical metrological behavior, but their physical meaning is often tied to a particular narrative, such as, segmented dynamics or discrete…
We derive a connection between performance of estimators the performance of the ideal observer on related detection tasks. Specifically we show how Shannon Information for the task of detecting a change in a parameter is related to the…