Random low rank mixed states are highly entangled

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.

12 pages, no figure. Title and main theorem changed, we emphasize that random low rank mixed states have high Schmidt numbers in v2