Related papers: Classical Geometric Fluctuation Relations
In this paper, we investigate the stochastic thermodynamics of Fisher information (FI), meaning we characterize both the \textit{fluctuations} of FI, introducing a parastatistics of that quantity, and thermodynamic quantities. We introduce…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
Standard quantum metrology relies on ensemble-averaged quantities, such as the Quantum Fisher Information (QFI), which often mask the fluctuations inherent to single-shot realizations. In this work, we bridge the gap between quantum…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
The Fisher information (FI) metric is a Riemannian metric that allows a geometric treatment of stochastic thermodynamics, introducing the possibility of computing thermodynamic lengths and deviations from equilibrium. At the trajectory…
Symmetric alpha-stable (S alpha S) distributions with alpha<2 lack finite classical Fisher information. Building on Johnson's framework, we define Mixed Fractional Information (MFI) via the initial rate of relative entropy dissipation…
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…
In estimating an unknown parameter of a quantum state the quantum Fisher information (QFI) is a pivotal quantity, which depends on the state and its derivate with respect to the unknown parameter. We prove the continuity property for the…
We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is…
Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of…
The basic properties of the Fisher information allow to reveal the statistical meaning of classical inequalities between mean functions. The properties applied to scale mixtures of Gaussian distributions lead to a new mean function of…
The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher Information (FI) has been evoked as a useful measure of sustainability and the variability of…
The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher…