Related papers: Fisher information and continuity estimates for no…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
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…
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.…
We analyze some parabolic PDEs with different drift terms which are gradient flows in the Wasserstein space and consider the corresponding discrete-in-time JKO scheme. We prove with optimal transport techniques how to control the L p and L…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
We consider kinetic models for Fermi-Dirac-like particles obeying the exclusion principle. A generalized notion of Fisher information, tailored to kinetic equations of Fermi-Dirac-Fokker-Planck type, is introduced via the associated entropy…
The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher…
Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the…
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…
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…
The JKO scheme provides the discrete-in-time approximation for the solutions of evolutionary equations with Wasserstein gradient structure. We study a natural space-discretization of this scheme by restricting the minimization to the…
Discrete events alter how parameter influence propagates in hybrid systems. Prevailing Fisher information formulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the…
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
We introduce a novel variant of the JKO scheme to approximate Darcy's law with a pressure dependent source term. By introducing a new variable that implicitly controls the source term, our scheme is still able to use the standard…
We consider the Fisher information for spatially homogeneous multi-species Landau system. We show that the mass-weighted Fisher information is monotone decreasing in time along the solutions of the Landau system with a general class of…
We prove L^$\infty$ estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such…
We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…
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 propose a new fully-discretized finite difference scheme for a quantum diffusion equation, in both one and two dimensions. This is the first fully-discretized scheme with proven positivity-preserving and energy stable properties using…