English

The positive partial transpose conjecture for n=3

Quantum Physics 2019-01-30 v2

Abstract

We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case n=3n=3 as a consequence of the fact that two-qutrit PPT states have Schmidt at most two. Our result in Lemma 3 is independent from the proof found M\"uller-Hermes. M\"uller-Hermes announced that this conjecture is true for the states on C3C3\mathbb{C}_3\otimes\mathbb{C}_3 \cite{hermes} recently. The PPT square conjecture in the case n4n\ge4 is still open.

Cite

@article{arxiv.1807.03636,
  title  = {The positive partial transpose conjecture for n=3},
  author = {Lin Chen and Yu Yang and Waishing Tang},
  journal= {arXiv preprint arXiv:1807.03636},
  year   = {2019}
}
R2 v1 2026-06-23T02:56:21.178Z