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Related papers: On a conjecture regarding Fisher information

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We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…

Quantum Physics · Physics 2009-02-20 Gabriel A. Durkin

In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cram\'er-Rao inequality is…

Quantum Physics · Physics 2023-01-18 Nour-Eddine Abouelkhir , Hanane EL Hadfi , Abdallah Slaoui , Rachid Ahl Laamara

Relativistic quantum metrology studies the maximal achievable precision for estimating a physical quantity when both quantum and relativistic effects are taken into account. We study the relativistic quantum metrology of temperature in…

High Energy Physics - Theory · Physics 2021-06-02 Haoxing Du , Robert B. Mann

A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-L\^e-Schwachh\"ofer. We introduce a…

Statistics Theory · Mathematics 2024-05-28 Kaori Yamaguchi , Hiraku Nozawa

In previous papers we have shown how Schrodinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The…

Quantum Physics · Physics 2023-11-13 Asher Yahalom

The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…

Quantum Physics · Physics 2021-03-15 Jianning Li , Haodi Liu , Zhihai Wang , Xuexi Yi

We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…

Quantum Physics · Physics 2026-04-29 Lei Wang

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…

Information Theory · Computer Science 2021-07-12 Leighton Pate Barnes , Ayfer Ozgur

The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time.…

Mathematical Physics · Physics 2009-11-10 Mark Naber

Quantum Fisher information and signal-to-noise ratio bounds are derived for the estimation of moments of general partially coherent objects. Under an asymptotic analysis in the sub-Rayleigh regime, these bounds are shown to be less…

Optics · Physics 2021-09-01 Kevin Liang , S. A. Wadood , A. N. Vamivakas

In recent years, in quantum information theory, there has been a remarkable development in the general theoretical framework for studying symmetry in dynamics. This development, called resource theory of asymmetry, is expected to have a…

Quantum Physics · Physics 2023-07-05 Daigo Kudo , Hiroyasu Tajima

By recourse to i) the Hellmann-Feynman theorem and ii) the Virial one, the information-optimizing principle based on Fisher's information measure uncovers a Legendre-transform structure associated with Schr\"odinger's equation, in close…

Statistical Mechanics · Physics 2015-05-27 S. P. Flego , A. Plastino , A. R. Plastino

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…

Information Theory · Computer Science 2010-07-12 Cihan Tepedelenlioglu , Mahesh K. Banavar , Andreas Spanias

We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…

Quantum Physics · Physics 2017-06-08 Marco G. Genoni

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…

Disordered Systems and Neural Networks · Physics 2024-09-12 Jakob Hüpfl , Felix Russo , Lukas M. Rachbauer , Dorian Bouchet , Junjie Lu , Ulrich Kuhl , Stefan Rotter

In open quantum systems, we study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. With the time evolution, for the initial atom…

Quantum Physics · Physics 2022-09-27 Mengge Zheng , Baoyuan Yang , Zixu Zhao

We analyze geometric terms and scaling properties of the Shannon mutual information in the continuum. This is done for a free massless scalar field theory in $d$-dimensions, in a coherent state reduced with respect to a general…

High Energy Physics - Theory · Physics 2017-06-28 David R. Junior , Luis E. Oxman

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…

Quantum Physics · Physics 2015-05-28 S. P. Flego , A. Plastino , A. R. Plastino

We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…

Statistical Mechanics · Physics 2020-07-01 Sosuke Ito , Andreas Dechant

The standard quantum coherence theory is defined with respect to an orthonormal basis of a Hilbert space. Recently, Bischof, Kampermann and Bru% \ss\ generalized the notion of coherence into the case of general measurements, and also, they…

Quantum Physics · Physics 2021-07-23 Jianwei Xu