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Related papers: Mutual Information Bounded by Fisher Information

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Quantum Fisher information is the principal tool used to give the ultimate precision bound on the estimation of parameters for quantum channels. In this work, we present analytical expressions for the quantum Fisher information with three…

Quantum Physics · Physics 2023-03-08 Lorenzo M. Procopio

The following problem is considered: given a joint distribution $P_{XY}$ and an event $E$, bound $P_{XY}(E)$ in terms of $P_XP_Y(E)$ (where $P_XP_Y$ is the product of the marginals of $P_{XY}$) and a measure of dependence of $X$ and $Y$.…

Information Theory · Computer Science 2019-03-12 Ibrahim Issa , Amedeo Roberto Esposito , Michael Gastpar

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…

Quantum Physics · Physics 2014-12-30 Tzu-Chao Hung

The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the…

Quantum Physics · Physics 2015-06-26 Kurt Jacobs

Since the cost of installing and maintaining sensors is usually high, sensor locations are always strategically selected. For those aiming at inferring certain quantities of interest (QoI), it is desirable to explore the dependency between…

Computation · Statistics 2019-06-05 Xiao Lin , Asif Chowdhury , Xiaofan Wang , Gabriel Terejanu

We study the bounds of mediated communication in sender-receiver games in which the sender's payoff is state-independent. We show that the feasible distributions over the receiver's beliefs under mediation are those that induce zero…

Theoretical Economics · Economics 2023-11-14 Roberto Corrao , Yifan Dai

Shannon-Hartley theorem can accurately calculate the channel capacity when the signal observation time is infinite. However, the calculation of finite-time mutual information, which remains unknown, is essential for guiding the design of…

Information Theory · Computer Science 2022-10-05 Jieao Zhu , Zijian Zhang , Zhongzhichao Wan , Linglong Dai

Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically…

Machine Learning · Statistics 2023-10-17 Paweł Czyż , Frederic Grabowski , Julia E. Vogt , Niko Beerenwinkel , Alexander Marx

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on…

Information Theory · Computer Science 2019-09-05 Maël Le Treust , Tristan Tomala

In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on…

Mathematical Physics · Physics 2013-01-18 J. -F. Bercher

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,…

Information Theory · Computer Science 2013-05-28 Jean-François Bercher

We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated…

Statistical Mechanics · Physics 2013-11-12 Takuya Yamano

We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…

Machine Learning · Statistics 2022-06-07 Jacques Balayla

Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…

Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves…

Machine Learning · Computer Science 2024-04-29 Rob Brekelmans , Sicong Huang , Marzyeh Ghassemi , Greg Ver Steeg , Roger Grosse , Alireza Makhzani

We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…

Statistics Theory · Mathematics 2022-08-25 Worachet Bukaew , Sikarin Yoo-Kong

Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…

Information Theory · Computer Science 2026-04-28 Mattia Carrino , Stefan Hohenegger

The Holevo quantity provides an upper bound for the mutual information between the sender of a classical message encoded in quantum carriers and the receiver. Applying the strong sub-additivity of entropy we prove that the Holevo quantity…

Quantum Physics · Physics 2015-05-18 Wojciech Roga , Mark Fannes , Karol Zyczkowski

Natural gradient descent, which preconditions a gradient descent update with the Fisher information matrix of the underlying statistical model, is a way to capture partial second-order information. Several highly visible works have…

Machine Learning · Computer Science 2020-06-09 Frederik Kunstner , Lukas Balles , Philipp Hennig

Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown ``signal'' belonging to a high-dimensional compact group, given noisy pairwise…

Statistics Theory · Mathematics 2025-12-23 Kaylee Y. Yang , Timothy L. H. Wee , Zhou Fan