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