In this paper, we compute the exact values of the minimum output entropy and the completely bounded minimal entropy of all quantum channels induced by Fourier multipliers acting on an arbitrary finite quantum group $\mathbb{G}$. We also give a sharp upper bound of the classical capacity which is an equality if $\mathbb{G}$ is a abelian group von Neumann algebra. Our results rely on a new and precise description of bounded Fourier multipliers from $\mathrm{L}^1(\mathbb{G})$ into $\mathrm{L}^p(\mathbb{G})$ for $1 < p \leq \infty$ where $\mathbb{G}$ is a co-amenable compact quantum group of Kac type and on the automatic completely boundedness of these multipliers that this description entails.

翻译：在本文中, 我们计算了由 Fourier 乘以任意的有限量组 $\ mathbb{G} 驱动的所有量子信道最小输出 的精确值和完全约束的最小值 。 如果$\ mathbb{G} $ 是 abelian group von Neumann 代数, 我们的计算结果依赖于从 $\ mathrm{L ⁇ 1 (\mathbb{G}) $\ mathrm{L}} p (\mathb{G}) $ 到 $ mathrm{L} p (\\ mathb{G}) $ 1 p p\ p\leq\ infty$ 。 如果 $\ mathb{ G} $ 是 Kac 的可共用压缩量组, 并且根据这些倍数的自动完全约束性。