On multipartite entanglement and multipartite correlations
Szilárd Szalay, Wigner Research Centre for Physics, Budapest, Hungary.

We briefly review the partial separability based classification of mixed
states of multipartite quantum systems of arbitrary number of subsystems.
We show how this structure simplifies in the case when not entanglement
but correlation is considered.
As special cases, we consider the notions of k-separability and
k-producibility (as well as their correlational versions), reveal how
these are dual to each other, and discuss some consequences.
We also give the corresponding multipartite correlation and entanglement
monotones, being the natural generalizations of mutual information,
entanglement entropy, entanglement of formation, or relative entropy of
entanglement, showing the same lattice structure as the classification
(multipartite monotonicity).
As illustration, we show some examples coming from molecular-physics.

The talk is based on the works
[PhysRevA 92, 042329 (2015)],
[SciRep 7, 2237 (2017)}] and
[JPhysA 51, 485302 (2018)],
and on results unpublished yet.