Related papers: Quantum Information Entropies for the $\ell$-state…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces.…
In this letter we analyze the effect of the spin dimensionality of a physical system in two mathematical formulations of the uncertainty principle: a generalized Heisenberg uncertainty relation valid for all antisymmetric N-fermion…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
We consider the probability distribution when the monotonic function $F(X)$ of the independent variable $X$ takes the maximum or minimum expected value under the two constraints of a certain probability and a certain expected value of the…
We study the evolution of the nonlinear version of the Fisher information along the quasilinear heat equation. We also provide a nonlinear version of a recent functional inequality (Cie\'slak--Fuest--Hajduk--Sier\.z\k{e}ga, 2024),…
The quantum Fisher information of a quantum state with respect to a certain parameter quantifies the sensitivity of the quantum state to changes in that parameter. Maximizing the quantum Fisher information is essential for achieving the…
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…
We consider the Heisenberg uncertainty principle of position and momentum in 3-dimensional spaces of constant curvature $K$. The uncertainty of position is defined coordinate independent by the geodesic radius of spherical domains in which…
$\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schr\"{o}dinger equation in position space and the Fourier transform of the corresponding wave…
We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a $N$ qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in…
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…
Shannon entropy ($S$), Fisher information ($I$) and a measure equivalent to Fisher-Shannon complexity $(C_{IS})$ of a ro-vibrational state of diatomic molecules (O$_2$, O$_2^+$, NO, NO$^+$) with generalized Kratzer potential is analyzed.…
Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures…
Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic uncertainties in quantum states, Heisenberg's error-disturbance relation (EDR) has been commonly believed to be another aspect of the…
We derive the quantum Fisher information for entropy estimation in a Gibbs state and show that it equals the inverse of the heat capacity, which is dual to the temperature Fisher information given by the heat capacity divided by the square…
We introduce a pair of transformations, which are mutually inverse, acting on rather general classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as p-moments,…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We examine time dependent Schrodinger equation with oscillating boundary condition. More specifically, we use separation of variable technique to construct time dependent rationally extended Poschl-Teller potential (whose solutions are…
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…