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])