Related papers: Fisher Information for Inverse Problems and Trace …
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…
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…
In this paper we study the Fisher information metric on the space of the coupling constants on both sides of the duality between non-relativistic dipole field theories and string theory in Schr\"odinger spacetime. We consider the following…
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…
In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
In this brief paper we revisit the Fisher information content of cosmological power spectra or two-point functions of Gaussian fields in order to comment on the assumption of Gaussian estimators and the use of parameter-dependent covariance…
The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…
Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three…
This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of…
The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are…
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 dynamics of two variants of quantum Fisher information under decoherence are investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector.…
This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical…
In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
Starting from the Fisher matrix for counts in cells, I derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key assumption is that the inverse of the covariance of the galaxy counts is given by the…
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…
Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…