Degradability of Modified Landau-Streater Type Low-Noise Quantum Channels in High Dimensions

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 η-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(ε^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(ε^2) degradability across a broader spectrum of quantum channels.