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Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

Statistics Theory · Mathematics 2025-03-17 Nicolas Bousquet , Mélanie Blazère , Thomas Cerbelaud

Gaussian quantum channels are relevant operations in continuous variable systems. In general, given an arbitrary state, the action on it is well-known provided that the quantum channels are completely characterized. In this work, we…

Quantum Physics · Physics 2025-05-20 Jonas F. G. Santos , Carlos H. S. Vieira , Wilder R. Cardoso

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…

Probability · Mathematics 2024-08-20 Nguyen Tien Dung , Nguyen Thu Hang

This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…

Analysis of PDEs · Mathematics 2024-10-11 Peijun Li , Ying Liang , Xu Wang

The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact…

Cosmology and Nongalactic Astrophysics · Physics 2012-03-30 Franz Elsner , Benjamin D. Wandelt

This paper investigates an inverse potential problem for the stochastic heat equation driven by space-time Gaussian noise, which is spatially colored and temporally white. The objective is to determine the covariance operator of the random…

Probability · Mathematics 2025-02-10 Peijun Li , Xiangchan Zhu , Yichun Zhu

We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the literature by allowing one to completely dispense from…

Analysis of PDEs · Mathematics 2025-12-08 Jean-Baptiste Casteras , Marco Flaim , Léonard Monsaingeon

The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…

Quantum Physics · Physics 2024-04-30 Matteo Scandi , Paolo Abiuso , Jacopo Surace , Dario De Santis

Fisher-information inequalities have recently been used as operational witnesses of nonclassical metrological behavior, but their physical meaning is often tied to a particular narrative, such as, segmented dynamics or discrete…

Quantum Physics · Physics 2026-05-20 Jeongho Bang , Su-Yong Lee

We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…

Statistical Mechanics · Physics 2014-09-16 Matteo Polettini

Fisher information, lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement (Pezz\'{e} and Smerzi, Phys. Rev. Lett. 102, 100401). We use Fisher information to distinguish…

Quantum Physics · Physics 2009-05-05 Jian Ma , Xiaoguang Wang

Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system…

Information Theory · Computer Science 2009-03-12 M. Payaró , D. P. Palomar

Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…

Statistics Theory · Mathematics 2016-07-20 Hanne Kekkonen , Matti Lassas , Samuli Siltanen

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 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…

Quantum Physics · Physics 2014-06-20 Manabendra N. Bera

Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…

Methodology · Statistics 2022-08-04 Adam Lane

We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for $\Phi^\ast_{M_2(\mb)}(A,A^\ast,M_2(\mb),\eta)$, where $A\in M_2(\mb)$ is a $2\times 2$…

Operator Algebras · Mathematics 2007-05-23 Bin Meng

In quantum metrology, the parameter estimation accuracy is bounded by quantum Fisher information. In this paper, we present coherence measures in terms of (quantum) Fisher information by directly considering the post-selective non-unitary…

Quantum Physics · Physics 2023-07-06 Deng-hui Yu , Chang-shui Yu

We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…

Statistics Theory · Mathematics 2023-11-21 Natalia Bochkina , Jenovah Rodrigues

The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…

Information Theory · Computer Science 2018-05-30 Manuel Stein , Josef A. Nossek