Related papers: An information upper bound for probability sensiti…
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…
The quantity of interest in the classical Cram\'er-Rao theory of unbiased estimation (e.g., the Cram\'er-Rao lower bound, its exact attainment for exponential families, and asymptotic efficiency of maximum likelihood estimation) is the…
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is…
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A…
We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…
Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited…
We introduce a new measure of robustness for statistical estimators, which we call \emph{empirical sensitivity}. An estimator $\hat \theta$ has bounded empirical sensitivity if, with high probability over a dataset $X = (X_1, \dots, X_n)…
The high-dimensional parameter space of deep neural networks -- the neuromanifold -- is endowed with a unique metric tensor defined by the Fisher information. Reliable and scalable computation of this metric tensor is valuable for theorists…
We investigate behavior of the Fisher information matrix of general stable distributions. DuMouchel (1975, 1983) proved that the Fisher information of characteristic exponent \alpha diverges to infinity as \alpha approaches 2. Nagaev and…
We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
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…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
In point spread function (PSF) photometry, the selection of the fitting aperture radius plays a critical role in determining the precision of flux and background estimations. Traditional methods often rely on maximizing the signal-to-noise…
The Fisher information matrix (FIM) has long been of interest in statistics and other areas. It is widely used to measure the amount of information and calculate the lower bound for the variance for maximum likelihood estimation (MLE). In…
The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show…
Uncertainty relations represent a foundational principle in quantum mechanics, imposing inherent limits on the precision with which \textit{mechanically} conjugate variables such as position and momentum can be simultaneously determined.…
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first…
This work unifies the equilibrium and non-equilibrium frameworks of quantum metrology within the context of many-body systems. We investigate dynamic sensing schemes to derive an upper bound on the quantum Fisher information for probe…
The quantum Fisher information, the quantum analogue of the classical Fisher information, is a central quantity in quantum metrology and quantum sensing due to its connection to parameter estimation and fidelity susceptibility. Using…