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

• URL: http://arxiv.org/abs/2401.16312v2
• Date: Tue, 30 Jan 2024 05:04:50 GMT
• Title: Degradability of Modified Landau-Streater Type Low-Noise Quantum Channels in High Dimensions
• Authors: Yun-Feng Lo, Yen-Chi Lee, Min-Hsiu Hsieh
• Abstract summary: We introduce and examine the Modified Landau-Streater (MLS) channels. These channels expand upon the qubit depolarizing and the recently proposed modified Werner-Holevo channels. Our results enhance the understanding of super-additivity in quantum channels within the low-noise regime.
• Score: 10.720038857779135
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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