We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent--also called reliability function--is equal to the well-known sphere packing bound, which can be written as a single-letter formula optimized over Petz-R\'enyi divergences. Remarkably, there is no critical rate and as such our characterization remains tight for arbitrarily low rates below the capacity. On the achievability side, we further extend our results to fully quantum channels. Our proofs rely on semi-definite program duality and a dual representation of the Petz-R\'enyi divergences via Young inequalities.

翻译：我们针对激活非信号关联辅助的经典-量子信道编码的误差指数给出了紧致的渐近刻画。具体而言，我们发现最优指数——亦称为可靠性函数——等于著名的球堆积界，该界可表示为通过Petz-Rényi散度优化的单字母公式。值得注意的是，该刻画不存在临界速率，因此在低于容量的任意低速率下仍保持紧致性。在可达性方面，我们进一步将结果推广至全量子信道。证明过程依赖于半定规划对偶性以及通过杨氏不等式得到的Petz-Rényi散度对偶表示。