Related papers: An approximate quantum Cram\'{e}r--Rao bound based…
This study presents the Fisher information for the position-dependent mass Schr\"odinger equation with hyperbolical potential {$V(x)=-V_0{\rm csch}^2(ax)$}. The analysis of the quantum-mechanical probability for the ground and exited states…
Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
Enhancing the precision of a measurement requires maximizing the information that can be gained about the quantity of interest from probing a system. For optical based measurements, such an enhancement can be achieved through two…
The first step of quantum measurement procedure is known as \emph{premeasurement}, during when correlation between measuring system and measurement apparatus is established. One compelling non-classical correlation is entanglement, a useful…
The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory. In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partite quantum…
Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…
Estimation of parameters is a pivotal task throughout science and technology. Quantum Cram\'{e}r-Rao bound provides a fundamental limit of precision allowed to achieve under quantum theory. For closed quantum systems, it has been shown how…
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…
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…
It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramer-Rao bound (CRB), a popular tool to lower bound the…
The quantum Cram\'er-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a…
We obtain the accuracy limit for estimating the expectation value of the position of a relativistic particle for an observer moving along one direction at a constant velocity. We use a specific model of a relativistic spin-1/2 particle…
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…
Worst-case bounds on the expected shortfall risk given only limited information on the distribution of the random variables has been studied extensively in the literature. In this paper, we develop a new worst-case bound on the expected…
The Cram\'er-Rao bound and the quantum Fisher information have been tools used extensively for interferometric phase sensitivity. Most scenarios considering a Mach-Zehnder interferometer with two input sources focused on the phase-matched…
The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…
Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes…