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Quantum channel capacity is a fundamental quantity in order to understand howgood can quantum information be transmitted or corrected when subjected tonoise. However, it is generally not known how to compute such quantities, sincethe 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 factthat the regularized coherent information of $n$ channel uses exceeds one-shotcoherent information. In this article, we study how the gain in quantumcapacity of qudit depolarizing channels relates to the dimension of the systemsconsidered. We make use of an argument based on the no-cloning bound in orderto proof that the possible superadditive effects decrease as a function of thedimension for such family of channels. In addition, we prove that the capacityof the qudit depolarizing channel coincides with the coherent information when$d\rightarrow\infty$. We also discuss the private classical capacity and obainsimilar results. We conclude that when high dimensional qudits experiencingdepolarizing noise are considered, the coherent information of the channel isnot only an achievable rate but essentially the maximum possible rate for anyquantum block code.

The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels