Leveraging magic resources for quantum channel capacity enhancement under stabilizer convolution

In this paper, we focus on discrete-variable quantum systems of odd prime dimension. We investigate the quantum capacity of stabilizer convolution channels under a variety of environmental states. Inspired by the recent result of Bu and Jaffe [Phys. Rev. Lett. 134, 050202 (2025)], our main contribution is to generalize the analysis beyond the discrete beam splitter---which is only applicable for odd prime dimensions $d\ensuremath{\ge}7$---to broader classes of stabilizer convolutions, allowing us to explore the behavior of magic resources in lower dimensions such as $d=3$ and $d=5$, where their role in enhancing quantum capacity has remained unclear. In fact, many of our mathematical results are derived under the broader setting of positive convolutions, not limited strictly to stabilizer convolutions.