Compatibility conditions from multipartite entanglement measures
  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. 
Jian-Ming Cai, Zheng-Wei Zhou, Shun Zhang and Guang-Can Guo