# Maximum $N$-body correlations do not in general imply genuine multipartite entanglement

## TL;DR

This paper demonstrates that strong N-party correlations in quantum systems do not necessarily indicate genuine multipartite entanglement, especially in high-dimensional systems, challenging common assumptions in quantum correlation analysis.

## Contribution

The authors introduce new tools for analyzing the Bloch representation to distinguish between correlation strength and entanglement in multipartite quantum states.

## Key findings

- Strong N-party correlations can occur without genuine multipartite entanglement in high-dimensional systems.
- In qubit systems, the GHZ state uniquely exhibits maximal N-party correlations and entanglement.
- Tensor products of Bell states can have strong correlations but lack genuine multipartite entanglement.

## Abstract

The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong $N$-party correlations with $N$-party entanglement in an $N$-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest $N$-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest $N$-party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation.