Related papers: Fisher information and Hamilton's canonical equati…
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…
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of…
Quantum sensors driven into the quantum chaotic regime can have dramatically enhanced sensitivity, which, however, depends intricately on the details of the underlying classical phase space. Here, we develop an accurate semiclassical…
Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a…
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 matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality,…
Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…
Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…
The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…
In this work, we study the dynamics of the logistic map based on a probabilistic characterization in terms of the invariant density. We analyze the relevant regimes of the dynamics (regular, oscillatory, onset chaotic and fully chaotic) in…
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…
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…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
This paper provides a systematic approach to semiparametric identification that is based on statistical information as a measure of its "quality". Identification can be regular or irregular, depending on whether the Fisher information for…