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arXiv · 0911.0879

When is there a multipartite maximum entangled state?

Runyao Duan·Yaoyun Shi
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Abstract

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 $d_1\geΠ_{i=2}^n d_i$, 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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Runyao Duan, Yaoyun Shi. 2009-11-04. When is there a multipartite maximum entangled state?. https://arxiv.org/abs/0911.0879

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