The detection of multipartite entanglement in multipartite quantum systems is
a fundamental and key issue in quantum information theory. In this paper, we
investigate k-nonseparability and k-partite entanglement of N-partite
quantum systems from the perspective of the generalized Wigner-Yanase skew
information introduced by Yang etal.
[\href{https://doi.org/10.1103/PhysRevA.106.052401 }{Phys. Rev. A \textbf{106},
052401 (2022)}]. More specifically, we develop two different approaches in form
of inequalities to construct entanglement criteria, which are expressed in
terms of the generalized Wigner-Yanase skew information. Any violation of these
inequalities by a quantum state reveals its k-nonseparability or k-partite
entanglement, so these inequalities present the hierarchic classifications of
k-nonseparability or k-partite entanglement for all N-partite quantum
states from N-nonseparability to 2-nonseparability or from 2-partite
entanglement to N-partite entanglement, which are more refined than
well-known ways.
It is shown that our results reveal some k-nonseparability and k-partite
entanglement that remain undetected by other methods, and these are illustrated
through some examples.Comment: 12 pages, 2 figure