Related papers: Fisher Information and Mutual Information Constrai…

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…

In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…

We consider natural and general exponential families $(Q_m)_{m\in M}$ on $\mathbb{R}^d$ parametrized by the means. We study the submodels $(Q_{\theta m_1+(1-\theta)m_2})_{\theta\in[0,1]}$ parametrized by a segment in the means domain,…

This paper proposes an alternative approach for constructing invariant Jeffreys prior distributions tailored for hierarchical or multilevel models. In particular, our proposal is based on a flexible decomposition of the Fisher information…

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,…

Fundamental relations between information and estimation have been established in the literature for the continuous-time Gaussian and Poisson channels, in a long line of work starting from the classical representation theorems by Duncan and…

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…

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…

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…

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…

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…

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…

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized $q$-Gaussian…

Consider two forms of sampling from a population: (i) drawing $s$ samples of $n$ elements with replacement and (ii) drawing a single sample of $ns$ elements. In this paper, under the setting where the descending order population frequency…

We study the mixing time guarantee for sampling in relative Fisher information via the Proximal Sampler algorithm, which is an approximate proximal discretization of the Langevin dynamics. We show that when the target probability…

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…

Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…

Van Trees inequality, also known as the Bayesian Cram\'er-Rao lower bound, is a powerful tool for establishing lower bounds for minimax estimation through Fisher information. It easily adapts to different statistical models and often yields…

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…