  Quantum secret sharing is well known as a method for players to share a
classical secret for secret sharing in quantum mechanical ways. Most of the
results associated with quantum secret sharing are based on pure multipartite
entangled states. In reality, however, it is difficult for players to share a
pure entangled state, although they can share a state close to the state. Thus,
it is necessary to study how to perform the quantum secret sharing based on a
general multipartite state. We here present a quantum secret sharing protocol
on an $N$-qubit state close to a pure $N$-qubit Greenberger-Horne-Zeilinger
state. In our protocol, $N$ players use an inequality derived from the Mermin
inequality to check secure correlation of classical key bits for secret
sharing. We show that if our inequality holds then every legitimate player can
have key bits with positive key rate. Therefore, for sufficiently many copies
of the state, the players can securely share a classical secret with high
probability by means of our protocol.
