  The hierarchy of nonlocality and entanglement in multipartite systems is one
of the fundamental problems in quantum physics. We study this topic in
three-qubit systems considering the entanglement classification of stochastic
local operations and classical communication (SLOCC). The equivalence under
SLOCC divides threequbit states into separable, biseparable, W, and
Greenberger-Horne-Zeilinger (GHZ) classes. The W and GHZ are two subclasses of
genuine tripartite entanglement.We adopt the family of GHZ-symmetric states as
a research subject, which share the symmetries of the GHZ state and have a
complete characterization of SLOCC classes. In the biseparable region (with
bipartite entanglement), there exist GHZ-symmetric states that are found to be
fully local. In addition, there are bilocal states in both theW and GHZ
classes. That is, neither of the subclasses of genuine tripartite entanglement
can ensure genuinely tripartite nonlocality.
