Concepts and Recent Advances in Generalized Information Measures and Statistics

1. Since the introduction of the information measure widely known as Shannon entropy, quantifiers based on information theory and concepts such as entropic forms and statistical complexities have ...
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Distances Measures for Probability Distributions

Pp. 130-146 (17)

Pedro W. Lamberti and Ana P. Majtey

Abstract

Many problems of statistical and quantum mechanics can be established in terms of a distance between probability distributions. The present work is devoted to review some of the most relevant applications of the notion of distance in the context of statistical mechanics, quantum mechanics and information theory. Although we make a general overview of the most frequently used distances between probability distributions, we will center our presentation in a distance known as the Jensen-Shannon divergence both in their classical and quantum versions. For the classical one we present its main properties and we discuss its relevance as a segmentation tool for symbolic sequences. In the quantum case we show that the quantum Jensen-Shannon divergence is an adequate measure of entanglement.

Keywords:

Probabilty distributions, Divergences, Geometry, Quantum mixed states, Entanglement.

Affiliation:

Facultad de Matematica, Astronomıa y Fısica, Universidad Nacional de C´ordoba and CONICET, Ciudad Universitaria, 5000 C´ordoba, Argentina