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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…

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…

The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate…

The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian…

With the help of the coherent states' basis we establish an interesting connection among i) the so-called Wehrl entropy, ii) Fisher's information measure $I$, and iii) the canonical ensemble entropy for the one-dimensional quantum harmonic…

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 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…

We study the classical and quantum Fisher information for the Lieb-Liniger model. The Fisher information has been studied extensively when the parameter is inscribed on a quantum state by a unitary process, e.g., Mach-Zehnder or Ramsey…

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…

Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…

We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…

Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…

The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…

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…

Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all…

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…

We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…

We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…