This paper delves into the degradability of quantum channels, with a specific focus on high-dimensional extensions of qubit depolarizing channels in low-noise regimes. We build upon the foundation of $\eta$-approximate degradable channels, as established by Sutter et al. and Leditzky et al., to introduce and examine the Modified Landau-Streater (MLS) channels. These channels expand upon the qubit depolarizing and the recently proposed modified Werner-Holevo channels by Roofeh and Karimipour, extending them to higher-dimensional Hilbert spaces (with dimension $d=2j+1$, where $j$ are positive half-integers). Our investigation centers on their conformity to the $O(\varepsilon^2)$ degradability pattern, aligning with and extending Leditzky et al.'s findings in the $d=2$ case. By replacing the SU($2$) generators with SU($d$) in our treatment, we may explore the potential inclusion of generalized Gell-Mann matrices in future research. Our results enhance the understanding of super-additivity in quantum channels within the low-noise regime and lay the groundwork for future explorations into conditions and structures that could lead to $O(\varepsilon^2)$ degradability across a broader spectrum of quantum channels.

翻译：本文深入探讨了量子通道的可退化性，特别关注低噪声区域中量子比特退极化通道的高维推广。我们以 Sutter 等人及 Leditzky 等人建立的 $\eta$-近似可退化通道为基础，引入并研究了修正型 Landau-Streater (MLS) 通道。这些通道将量子比特退极化通道及 Roofeh 与 Karimipour 最近提出的修正型 Werner-Holevo 通道推广到更高维的希尔伯特空间（维度 $d=2j+1$，其中 $j$ 为半整数正数）。我们的研究聚焦于它们对 $O(\varepsilon^2)$ 可退化模式的符合性，这既与 Leditzky 等人在 $d=2$ 情况下的发现一致，又对其进行了推广。通过在处理方法中将 SU($2$) 生成元替换为 SU($d$)，我们为未来研究引入广义盖尔曼矩阵的可能性奠定了基础。我们的结果加深了对低噪声区域中量子通道超可加性的理解，并为未来探索可能产生更广泛量子通道 $O(\varepsilon^2)$ 可退化性的条件与结构奠定了基础。