When is there a multipartite maximum entangled state?

Details When is there a multipartite maximum entangled state? When is there a multipartite maximum entangled state?

2009-11-04

arxiv.org/abs/0911.0879v1

Physics

Quantum Physics

10 pages, no figure. We know the answer is quite simple, but the proof is somewhat involved. Comments are welcome

Scientific paper

For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes... d_n$, $d_1\ge d_2\ge...\ge d_n$, is there an entangled state {\em 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 $d_1\ge\Pi_{i=2}^n d_i$, 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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