Correlations in quantum systems can be much stronger than in classicalones, an important manifestation of this is quantum entanglement.
States of a bipartite system (either pure or mixed) can be either
uncorrelated or correlated, while for more-than-two-partite systems this
situation is getting complicated and many different kinds of
correlations arise.
In the talk,
(i) we show how to grasp this complicated structure efficiently,
(ii) we define proper correlation measures, by the use of which
(iii) we formulate the multipartite correlation based clustering of the
system,
(iv) and we give an efficient algorithm for this.
The importance of the latter two points is that the existence of higher
correlations makes the bipartite correlation based ("graph theoretical")
clustering insufficient.
(v) We also illustrate the multipartite correlation theory by showing
some examples coming from molecular-physics. This field provides an
excellent playground for multipartite correlation theory, since here the
ground states of the many-body interacting Hamiltonians are naturally
factorized into approximate products of clusters of localized orbitals.

Ref.:
Phys. Rev. A 92, 042329 (2015) (arXiv:1503.06071 [quant-ph])