  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.
