AI 中文总结
本文研究双体态凸集面的局部几何，利用相关文献结果明确一般子空间下施密特数见证的存在条件，并进一步证明超出阈值的见证在特定投影态附近存在。
AI 中文摘要
设$F_E$是所有$m\otimes n$双体态凸集的面，由范围包含于子空间$E$的态构成。对于特定维度的一般子空间$E$，我们利用[Phys. Rev. A 112 (2025), 032426]的结果可知，存在仅依赖$E$维度的数$\u03ba$，使得在$F_{E^\u27c2}$之外存在施密特数$\u2113$见证当且仅当$\u2113\leq\u03ba$。在该一般情形下，本文证明：对于$\u2113>\u03ba$，在位于$F_{E^\u27c2}$中心的投影态附近存在施密特数$\u2113$见证。
英文摘要
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 $κ$, depending only on the dimension of $E$, such that there exist Schmidt number $\ell$ witnesses outside of $F_{E^\perp}$ if and only if $\ell\leκ$. In this generic case, we show in this paper that there exist Schmidt number $\ell$ witnesses for $\ell>κ$ around the projection states located at the center of $F_{E^\perp}$.
Comments13 pages, 5 figures
