Related papers: Information metric from Riemannian superspaces

Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positive-definite quaternion matrices. In order to do so, it…

We put forward several information-theoretic measures for analyzing the uncertainty of fermionic phase-space distributions using the theory of supernumbers. In contrast to the bosonic case, the anticommuting nature of Grassmann variables…

In this short note, we examine geodesic distance in Fisher information space in which the metric is defined by the entanglement entropy in CFT_(1+1). It is obvious in this case that the geodesic distance at a constant time is a function of…

This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a…

We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…

We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the…

We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first construction is based on a dynamic variational formulation in…

Preconditioning with the quantum Fisher information matrix (QFIM) is a popular approach in quantum variational algorithms. Yet the QFIM is costly to obtain directly, usually requiring more state preparation than its classical counterpart:…

Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold…

This is a review of the ideas behind the Fisher--Rao metric on classical probability distributions, and how they generalize to metrics on density matrices. As is well known, the unique Fisher--Rao metric then becomes a large family of…

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…

Csiszar's f-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semidefinite matrices are in the place of probability distributions and the quantum…

We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism.…

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…

We show that two quantities in quantum metrology that were thought to be the same, the quantum Fisher information matrix and the Bures metric, are not the same. They differ at points at which the rank of the density matrix changes. The…

Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…

We consider the problem of estimating an arbitrary dynamical parameter of an quantum open system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be…

In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In…