Degradability of Modified Landau-Streater Type Low-Noise Quantum Channels in High Dimensions
This work addresses the degenerability of the Modified Landau–Streater (MLS) quantum channel in high-dimensional Hilbert spaces. Specifically, we consider the $d$-dimensional ($d = 2j+1$, odd) MLS channel induced by the SU(2) spin-$j$ representation—a higher-dimensional generalization of the qubit depolarizing channel and the modified Werner–Holevo channel—and construct its SU($d$)-symmetric form for the first time, analyzing it systematically. Leveraging the $eta$-approximate degenerability framework, we combine SU($d$) Lie algebra representations, the generalized Gell-Mann matrix basis, and perturbative expansion to rigorously prove that the channel is $O(varepsilon^2)$-degradable under low-noise strength $varepsilon$. This extends Leditzky et al.’s qubit result to all odd dimensions, thereby deepening the understanding of superadditivity of classical capacity in low-noise regimes and establishing a general structural paradigm for constructing families of $O(varepsilon^2)$-degradable channels in arbitrary odd dimensions.