# Multipartite correlations in mutually unbiased bases

## TL;DR

This paper introduces new measures of multipartite quantum correlations based on classical correlations in mutually unbiased bases, providing operationally meaningful metrics and applications in entanglement detection.

## Contribution

It proposes novel correlation measures rooted in classical mutual information within mutually unbiased bases and identifies conditions for their maximization, linking to important quantum states.

## Key findings

- Maximized correlation measures for key quantum states.
- New criteria for detecting high-dimensional tripartite entanglement.
- Operational interpretation of classical correlations in quantum bases.

## Abstract

We introduce new measures of multipartite quantum correlations based on classical correlations in mutually unbiased bases. These classical correlations are measured in terms of the classical mutual information, which has a clear operational meaning. We present sufficient conditions under which these measures are maximized. States that have previously been shown to be particularily important in the context of LOCC transformations fulfill these conditions and therefore maximize the correlation measures. In addition, we show how the new measures can be used to detect high-dimensional tripartite entanglement by using only a few local measurements.