A generalized quantum relative entropy

Abstract

We propose a generalization of the quantum relative entropy by considering the geodesic on a manifold formed by all the invertible density matrices P. This geodesic is defined from a deformed exponential function ϕ which allows to work with a wider class of families of probability distributions. Such choice allows important flexibility in the statistical model. We show and discuss some properties of this proposed generalized quantum relative entropy.2020 Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

New power-law tailed distributions emerging in $κ$-statistics

“…Over the last two decades, the κ-statistical theory has attracted the interest of many researchers, who have studied its foundations [5][6][7][8][9][10], and the underlying thermodynamics [11][12][13][14][15], and at the same time, have considered specific applications of the theory to various fields of science. A nonexhaustive list of applications includes, among others, those in quantum statistics [16][17][18], in quantum theory [19][20][21], in plasma physics [22][23][24][25][26][27][28], in nuclear fission [29,30], in particle physics [31], in astrophysics [32][33][34][35][36], in cosmology [37][38][39][40][41][42][43], in geomechanics [44,45], in genomics [46,47], in complex networks [48,49], in waveform inversion algorithms [50], in image processing…”

Conditions for the existence of a generalization of Rényi divergence

“…To cite a few, the usage of divergence metric has been considered in several domains such as statistics (including statistical physics) and learning [19,10,20,21], econometrics [22,23,24,25,26], digital communications [27,28,29,30], signal and image processing [31,32,33], biomedical processing [34]. Also, quantum versions of generalized divergences are of interest in the literature [35,36].…”