When is there a multipartite maximum entangled state?  (pp0925-0935)
          Runyao Duan and Yaoyun Shi 
          doi:https://doi.org/10.26421/QIC10.11-12-3
Abstracts: For a multipartite quantum system of the dimension d1 X d2 X · · · X dn, where d1 ≥ d2 ≥ · · · ≥ dn ≥ 2, is there an entangled state maximum in the sense that all other states in the system can be obtained from the state through local quantum operations and classical communications (LOCC)? When d1 ≥ Πn i=2di, such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.
Key words: quantum information theory, quantum communication protocol,tensor rank, maximum entangled state, stochastic entanglement transformation