# Quantifying genuine multipartite correlations and their pattern complexity

## TL;DR

This paper introduces an information-theoretic framework to quantify and classify genuine multipartite correlations in classical and quantum systems, providing tools to measure correlation amounts and pattern complexities.

## Contribution

It develops measures for genuine multipartite correlations and introduces the concept of weaving to classify correlation pattern complexities.

## Key findings

- Defined measures for genuine multipartite correlations.
- Introduced the concept of weaving to classify correlation patterns.
- Provided a framework applicable to classical and quantum systems.

## Abstract

We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as: what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e. statistical dependencies which cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states which display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.