English

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.

Keywords

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

R2 v1 2026-07-22T19:32:46.134Z