# Geometric Measures of Information for Quantum State Characterization

## TL;DR

This paper explores geometric measures like information area and volume derived from classical information theory concepts, discussing their potential applications in quantum information processing.

## Contribution

It introduces geometric measures such as information area and higher-dimensional volumes, extending classical entropic measures for potential use in quantum information.

## Key findings

- Defined an information area analogous to entropic measures.
- Extended geometric measures to higher dimensions.
- Discussed potential applications in quantum information processing.

## Abstract

We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information distance formula of Rokhlin and Rajski. We then define an analogous information area. We motivate this definition and discuss its properties. We extend this definition to higher-dimensional volumes. We briefly discuss the potential utility for these geometric measures in quantum information processing.