相关论文: A Lower Bound for the Fisher Information Measure
Informationally complete measurements form the foundation of universal quantum state reconstruction, while quantum parameter estimation is based on the local structure of the manifold of quantum states. Here we establish a general link…
We introduce new classes of informational functionals, called \emph{upper moments}, respectively \emph{down-Fisher measures}, obtained by applying classical functionals such as $p$-moments and the Fisher information to the recently…
The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we…
An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be analytically calculated and…
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal…
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…
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…
Fisher's exact test is often a preferred method to estimate the significance of statistical dependence. However, in large data sets the test is usually too worksome to be applied, especially in an exhaustive search (data mining). The…
Accessible information, which is a basic quantity in quantum information theory, is computed for a general quantum Gaussian ensemble under certain "threshold condition". It is shown that the maximizing measurement is Gaussian, constituting…
In this article, we present recent developments of information geometry, namely, geometry of the Fisher metric, dualistic structures and divergences on the space of probability measures, particularly the theory of geodesics of the Fisher…
We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information.…
The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…
When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff…
The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…
Any imaging device such as a microscope or telescope has a resolution limit, a minimum separation it can resolve between two objects or sources; this limit is typically defined by "Rayleigh's criterion", although in recent years there have…
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A…
Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…
The quantum information and the Bures metric are equivalent to each other, except at points where the rank of the density matrix changes. Here we show that by slightly modifying the definition of the Bures metric, the quantum information…