EPJ Plus Focus Point on Classical and Quantum Information Geometry

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Published on 25 May 2021

What is information? What can we do with information? How are we supposed to understand information? How does information influence the development of modern Science?

Some, if not all and a thousand more, of these questions come to the mind of almost every modern researcher whose research area is somehow interconnected with Information Theory. However, the answers to these questions are far from being completely unravelled, and some recent theoretical developments seem to suggest that our understanding of the geometrical aspects of Information Theory will play an increasingly important role in the quest for answers.

The interplay between Differential Geometry, Mathematical Statistics, Probability Theory and Quantum Mechanics resulting in the so-called field of (Classical and Quantum) Information Geometry represents one of the most effective examples of cross-fertilizations of modern Science. The powerful language of Differential Geometry in its modern, coordinate-free formulation represents the perfect tool for understanding deep conceptual aspects, and, at the same time, allows to present explicit computations in a neat and elegant way.

The aim of this Focus Point is to present some of the more recent developments in the framework of Classical and Quantum Information Geometry to readers who have different scientific backgrounds and work in different fields of application of Information Geometry, hoping to contribute a little more to the transversal spreading of this beautiful subject.

The Editors
Florio M. Ciaglia (Max Planck Institute for Mathematics in the Sciences, Leipzig)
Stefano Mancini (University of Camerino)
Ha Quang Minh (RIKEN Center for Advanced Intelligence Project, Tokyo)

All articles are available here and are freely accessible until 19 July 2021. For further information read the Editorial.