  In this paper, we focus on two different kinds of multipartite correlation,
$k$-nonseparability and $k$-partite entanglement, both of which can describe
the essential characteristics of multipartite entanglement. We propose
effective methods to detect $k$-nonseparability and $k$-partite entanglement in
terms of quantum Fisher information. We illustrate the significance of our
results and show that they identify some $k$-nonseparability and $k$-partite
entanglement that cannot be identified by known criteria by several concrete
examples.
