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Random low rank mixed states are highly entangled

Hao Chen
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Abstract

We prove that for many ranks r<2m-2, random rank r mixed states in bipartite mxm systems have relatively high Schmidt numbers, which is based on algebraic-geometric separability criterion proved in [1]. This also means that the algebraic-geometric separability criterion can be used to detect all low rank entangled mixed states outside a measure zero set.

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Hao Chen. 2001-11-13. Random low rank mixed states are highly entangled. https://arxiv.org/abs/quant-ph/0111004

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