相关论文: Jensen-Shannon divergence, Fisher information, and…

We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the…

We analyze the Shannon and Fisher information measures for systems subjected to quartic and symmetric potential wells. The wave functions are obtained by solving the time-independent Schr\"{o}dinger equation, using aspects of perturbation…

In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…

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…

Connections between Fisher information, Kaehler geometry of a quantum projective Hilbert space, and the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter are sketched.

Distance covariance is a measure of dependence between two random variables that take values in two, in general different, metric spaces, see Sz\'ekely, Rizzo and Bakirov (2007) and Lyons (2013). It is known that the distance covariance,…

There are three classical divergence measures in the literature on information theory and statistics, namely, Jeffryes-Kullback-Leiber's J-divergence, Sibson-Burbea-Rao's Jensen-Shannon divegernce and Taneja's arithemtic-geometric mean…

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…

In this work, a scattering process of quantum particles through a potential barrier is considered. The statistical complexity and the Fisher-Shannon information are calculated for this problem. The behaviour of these entropy-information…

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…

The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions. In this work, we introduce an alternative definition of the…

Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…

Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it…

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…

We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…

We analyze geometric terms and scaling properties of the Shannon mutual information in the continuum. This is done for a free massless scalar field theory in $d$-dimensions, in a coherent state reduced with respect to a general…

The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the quantum isotropic harmonic oscillator. We show that these magnitudes are independent of…

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs' paradox. Granted that it is as much at home in classical as in quantum statistical…

The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…