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Related papers: A Lower Bound for the Fisher Information Measure

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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

We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of…

Statistics Theory · Mathematics 2007-06-13 Alessandra Luati

In this work, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI…

Quantum Physics · Physics 2021-12-03 Akira Sone , M. Cerezo , Jacob L. Beckey , Patrick J. Coles

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…

Probability · Mathematics 2012-05-01 S. G. Bobkov , G. P. Chistyakov , F. Götze

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…

Quantum Physics · Physics 2013-12-06 Katarzyna Macieszczak

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…

Quantum Physics · Physics 2017-08-02 Yu Chen , Haidong Yuan

The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…

Information Theory · Computer Science 2021-06-11 Manuel S. Stein

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…

General Relativity and Quantum Cosmology · Physics 2011-11-08 Michele Vallisneri

Quantum Fisher information (QFI) plays a vital role in quantum precision measurement, quantum information, many-body physics, and other domains. Obtaining the QFI from experiment for a quantum state reveals insights such as the limits of…

Quantum Physics · Physics 2024-08-26 Qi Liu

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear)…

Statistics Theory · Mathematics 2012-11-22 Ngai Hang Chan , Ching-Kang Ing

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

For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for…

Quantum Physics · Physics 2014-12-25 Tzu-Chao Hung

A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of…

Quantum Physics · Physics 2018-01-25 Huangjun Zhu , Masahito Hayashi

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…

Information Theory · Computer Science 2022-07-12 Jiannan Yang

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…

Probability · Mathematics 2024-09-23 Nguyen Tien Dung

The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…

We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…

Quantitative Methods · Quantitative Biology 2025-05-14 Michał Komorowski

Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…

Quantum Physics · Physics 2020-04-22 Shingo Kukita

The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles…

The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap…

Quantum Physics · Physics 2013-05-29 Rafal Demkowicz-Dobrzanski