Distances between probabilities distributions

A.P. MAJTEY; P.W. LAMBERTI

Recent Advances in Generalized Information Measures and Statistics

Kowalski, Rossignoli & Curado (Eds.), Bentham Science Books

Año: 2010;

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 relevantapplications 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 distancesbetween 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 presentits 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 ofentanglement.