Related papers: Pointwise mutual information bounded by stochastic…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
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…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
The problem how to approximately determine the absolute value of the Fisher information measure for a general parametric probabilistic system is considered. Having available the first and second moment of the system output in a parametric…
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…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
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 derive upper bounds on the quantum Fisher information in interferometry with $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence of arbitrarily correlated Gaussian dephasing including independent and collective…
Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…
The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
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…
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
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…
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…
We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states…