  In secret sharing protocols, a secret is to be distributed among several
partners so that leaving out any number of them, the rest do not have the
complete information. Strong multiqubit correlations in the state by which
secret sharing is carried out, had been proposed as a criterion for security of
such protocols against individual attacks by an eavesdropper. However we show
that states with weak multiqubit correlations can also be used for secure
secret sharing. That our state has weak multiqubit correlations, is shown from
the perspective of violation of local realism, and also by showing that its
higher order correlations are described by lower ones. We then present a
unified criterion for security of secret sharing in terms of violation of local
realism, which works when the secret sharing state is the
Greenberger-Horne-Zeilinger state (with strong multiqubit correlations), as
well as states of a different class (with weak multiqubit correlations).
