Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an unbounded number of channel uses. This leads to the phenomenon known as superadditivity, which refers to the fact that the regularized coherent information of $n$ channel uses exceeds one-shot coherent information. In this article, we study how the gain in quantum capacity of qudit depolarizing channels relates to the dimension of the systems considered. We make use of an argument based on the no-cloning bound in order to proof that the possible superadditive effects decrease as a function of the dimension for such family of channels. In addition, we prove that the capacity of the qudit depolarizing channel coincides with the coherent information when $d\rightarrow\infty$. We also discuss the private classical capacity and obain similar results. We conclude that when high dimensional qudits experiencing depolarizing noise are considered, the coherent information of the channel is not only an achievable rate but essentially the maximum possible rate for any quantum block code.

翻译：量子信道容量是理解量子信息在有噪声环境中传输或纠正能力的基本量。然而，由于量子信道的相干信息并非对所有信道均具有可加性，这意味着必须对无限次信道使用的相干信息进行最大化，因此通常无法直接计算该量。这导致了超可加现象，即n次信道使用的正则化相干信息超过单次相干信息。本文研究了qudit退极化信道量子容量的增益与系统维度的关系。我们基于不可克隆边界论证，证明了此类信道的超可加效应随维度增加而减小。此外，我们证明了当$d\rightarrow\infty$时，qudit退极化信道的容量与相干信息一致。同时讨论了私有经典容量并得到类似结果。结论表明：当考虑高维qudit经历退极化噪声时，信道的相干信息不仅是可达速率，本质上是任何量子分组码的最大可能速率。