Related papers: Quantum Skew Divergence
In this article we exploit the Bhattacharyya statistical divergence to determine the similarity of probability distributions of quantum observables. After brief review of useful characteristics of the Bhattacharyya divergence we apply it to…
We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing…
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for…
We examine the problem of controlling divergences for latent space regularisation in variational autoencoders. Specifically, when aiming to reconstruct example $x\in\mathbb{R}^{m}$ via latent space $z\in\mathbb{R}^{n}$ ($n\leq m$), while…
Kullback--Leibler (KL) divergence is a fundamental measure of the dissimilarity between two probability distributions, but it can become unstable in high-dimensional settings due to its sensitivity to mismatches in distributional support.…
A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is…
The Loewner equation, in its stochastic incarnation introduced by Schramm, is an insightful method for the description of critical random curves and interfaces in two-dimensional statistical mechanics. Two features are crucial, namely…
We consider typical experiments that use Bell-inequalities to test local-realist theories of quantum mechanics and gain insight into how certain results can be obtained. We see that results against local-realism arise from some `quantum…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
Nonclassical correlations are significant physical resources with extensive applications in quantum information processing. We introduce the modified Wigner-Yanase-Dyson skew information of a quantum state relative to a quantum channel, and…
The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations…
We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty…