  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.
