Random low rank mixed states are highly entangled
Quantum Physics
2007-05-23 v3
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.
Cite
@article{arxiv.quant-ph/0111004,
title = {Random low rank mixed states are highly entangled},
author = {Hao Chen},
journal= {arXiv preprint arXiv:quant-ph/0111004},
year = {2007}
}
Comments
12 pages, no figure. Title and main theorem changed, we emphasize that random low rank mixed states have high Schmidt numbers in v2