Abstract:
For a multipartite quantum system of the dimension d(1) circle times d(2) circle times ... circle times d(n), where d(1) >= d(2) >= ... >= d(n) >= 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 d(1) >= n i=2d(i), such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.
