When is there a multipartite maximum entangled state?

Publication Type:
Journal Article
Citation:
Quantum Information and Computation, 2010, 10 (11-12), pp. 925 - 935
Issue Date:
2010-11-01
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For a multipartite quantum system of the dimension d1 ⊗ d2 ⊗· ⊗ dn, where d1 ≥ d2 ≥ · ≥ d2, 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 ≥ ∏ni=2 di, such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.
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