Related papers: Probability measure generated by the superfidelity
We investigate some properties of density measures -- finitely additive measures on the set of natural numbers $\N$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the…
We present a universal technique for quantum state estimation based on the maximum-likelihood method. This approach provides a positive definite estimate for the density matrix from a sequence of measurements performed on identically…
Given a pure state vector |x> and a density matrix rho, the function p(x|rho)=<x|rho|x> defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to…
We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. We demonstrate that the fraction of linear subgraphs just below the percolation threshold is about 95\% of all finite subgraphs, and the…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
Probability densities that are not uniquely determined by their moments are said to be "moment-indeterminate", or "M-indeterminate". Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
This work deals with the issue of assessing the influence of a node in the entire network and in the subnetwork to which it belongs as well, adapting the classical idea of vertex centrality. We provide a general definition of relative…
Bures distance holds a special place among various distance measures due to its several distinguished features and finds applications in diverse problems in quantum information theory. It is related to fidelity and, among other things, it…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show…
A result of Zyczkowski and Sommers [J.Phys.A, 33, 2045--2057 (2000)] gives the eigenvalue probability density function for the top N x N sub-block of a Haar distributed matrix from U(N+n). In the case n \ge N, we rederive this result,…
In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Let $\left(\Omega,\Sigma,p\right)$ be a probability measure space and let $X:\Omega\to{\mathbb{R}}^k$ be a (vector valued) random variable. We suppose that the probability $p_X$ induced by $X$ is absolutely continuous with respect to the…