Related papers: Fisher information and asymptotic normality in sys…
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 consider the problems of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. On the identifiability question, we show that the knowledge of…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
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…
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…
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…
System identification is an integrant part of control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it…
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
Many real-world tasks include some kind of parameter estimation, i.e., determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic…
We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is…
We investigate the quantum parameter estimation in circuit quantum electrodynamics via dispersive measurement. Based on the Metropolis Hastings (MH) algorithm and the Markov chain Monte Carlo (MCMC) integration, a new algorithm is proposed…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
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 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…
Combining the ideas of quantum Fisher information and quantum renormalization group method, the Berezinskii-Kosterlitz-Thouless quantum phase transition of spin- 1/2 XXZ chain is investigated. Quantum Fisher informations of the whole N…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
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…