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arXiv · 2606.16265

Bi-qutrit entangled edge states of positive partial transposes with largest ranks

Kyung Hoon Han·Seung-Hyeok Kye
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Abstract

Whenever $E$ is an eight dimensional subspace of the bi-qutrit quantum system whose orthogonal complement is spanned by a vector of Schmidt rank three, we show that there exist PPT entangled edge states with the range space $E$ whose partial transposes are of rank six, which is the largest possible rank. In this way, we exhibit a huge family of bi-qutrit PPT entangled edge states of type $(8,6)$. They make faces of the convex set of all PPT states, and we find bi-qutrit PPT entangled edge states of other types on the boundaries of such faces.

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Kyung Hoon Han, Seung-Hyeok Kye. 2026-06-15. Bi-qutrit entangled edge states of positive partial transposes with largest ranks. https://arxiv.org/abs/2606.16265

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