Geometry of Information: classical and quantum aspects

TL;DR

This paper explores the categorification of information theory structures, covering classical and quantum probabilistic models, F-manifolds, and motivic enrichments, to deepen understanding of information geometry.

Contribution

It introduces a novel categorification framework for information theory structures, integrating classical and quantum models with advanced geometric and motivic concepts.

Findings

Unified perspective on classical and quantum probabilistic models

Emergence of F-manifolds in information geometry

Motivic enrichments offer new insights into information structures

Abstract

In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic enrichments.