  We consider an arbitrary d_{1}\otimes d_{2}\otimes ... \otimes d_{N}
composite quantum system and find necessary conditions for general m-party
subsystem states to be the reduced states of a common N-party state. These
conditions will lead to various monogamy inequalities for bipartite quantum
entanglement and partial disorder in multipartite states. Our results are
tightly connected with the measures of multipartite entanglement.
