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arXiv · 1807.03636

The positive partial transpose conjecture for n=3

Lin Chen·Yu Yang·Waishing Tang
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Abstract

We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case $n=3$ 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 $\mathbb{C}_3\otimes\mathbb{C}_3$ \cite{hermes} recently. The PPT square conjecture in the case $n\ge4$ is still open.

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Lin Chen, Yu Yang, Waishing Tang. 2018-07-07. The positive partial transpose conjecture for n=3. https://doi.org/10.1103/physreva.99.012337

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