We propose an iterative algorithm for computing the Petz-Augustin information of order $\alpha\in(1/2,1)\cup(1,\infty)$. The optimization error is guaranteed to converge at a rate of $O\left(\vert 1-1/\alpha \vert^T\right)$, where $T$ is the number of iterations. Let $n$ denote the cardinality of the input alphabet of the classical-quantum channel, and $d$ the dimension of the quantum states. The algorithm has an initialization time complexity of $O\left(n d^{3}\right)$ and a per-iteration time complexity of $O\left(n d^{2}+d^3\right)$. To the best of our knowledge, this is the first algorithm for computing the Petz-Augustin information with a non-asymptotic convergence guarantee.

翻译：我们提出了一种迭代算法，用于计算阶数 $\alpha\in(1/2,1)\cup(1,\infty)$ 的Petz-Augustin信息。该算法保证优化误差以 $O\left(\vert 1-1/\alpha \vert^T\right)$ 的速率收敛，其中 $T$ 为迭代次数。令 $n$ 表示经典-量子信道输入字母表的基数，$d$ 表示量子态的维度。该算法的初始化时间复杂度为 $O\left(n d^{3}\right)$，单次迭代时间复杂度为 $O\left(n d^{2}+d^3\right)$。据我们所知，这是首个具有非渐近收敛性保证的Petz-Augustin信息计算算法。