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arXiv · 2608.14199

Local geometry for Schmidt number witnesses

Young-Hoon Kiem·Seung-Hyeok Kye
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Abstract

Suppose that $F_E$ is the face of the convex set of all $m\otimes n$ bi-partite states which consists of states with ranges contained in a subspace $E$. For generic subspaces $E$ with a specific dimension, we use the result in [Phys. Rev. A 112 (2025), 032426] to see that there exists a number $\kappa$, depending only on the dimension of $E$, such that there exist Schmidt number $\ell$ witnesses outside of $F_{E^\perp}$ if and only if $\ell\le\kappa$. In this generic case, we show in this paper that there exist Schmidt number $\ell$ witnesses for $\ell>\kappa$ around the projection states located at the center of $F_{E^\perp}$.

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Young-Hoon Kiem, Seung-Hyeok Kye. 2026-08-14. Local geometry for Schmidt number witnesses. https://arxiv.org/abs/2608.14199

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