相关论文: Fisher's information for the position-dependent ma…
It is well known that a suggestive connection links Schr\"odinger's equation (SE) and the information-optimizing principle based on Fisher's information measure (FIM). It has been shown that this entails the existence of a Legendre…
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for…
We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…
We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies…
We propose a new generalised formalism for estimating the quantum phase uncertainty of pure and mixed continuous-variable quantum states and compare this with the phase uncertainty given by the quantum Fisher information. In order to…
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…
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…
We investigate the performance of entangled coherent state for quantum enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity.…
Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…
In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is…
We study the two dimensional system influenced by a non-central potential consisting of a Kratzer potential with a dipole moment, along with a vector potential of the Aharonov-Bohm (AB) effect. We explore various information theoretic…
We establish an a priori estimate for the dissipation of the Fisher information for the space-homogeneous Landau equation with very soft potentials. This work is motivated by the recent breakthrough by Guillen and Silvestre, which proves…
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry,…
We consider the Landau-Coulomb equation for initial data with bounded mass, finite numbers of moments, and entropy. We show the existence of a global weak solution that has bounded Fisher information for positive times. This solution is…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
We study the stability/instability of standing waves for the one dimensional nonlinear Schr\"odinger equation with double power nonlinearities: \begin{align*} &i\partial_t u +\partial_x^2 u -|u|^{p-1}u +|u|^{q-1}u=0, \quad (t,x)\in…
The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in…
The following comparison rules for the discrete spectrum of the position-dependent mass (PDM) Schroedinger equation are established. (i) If a constant mass $m_0$ and a PDM $m(x)$ are ordered everywhere, that is either $m_0\leq m(x)$ or…
We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and…
In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent…