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 letter, 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 superaditive 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 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:量子信道能力是一个基本数量,以便了解在受到噪音影响时,数量信息能如何很好地传播或纠正;然而,一般不知道如何计算此类数量,因为量子通道的一致性信息并不是所有渠道的添加物,意味着必须在无限制数量的频道使用量上将其最大化。这导致被称为超增加性的现象,即美元频道使用量的正常一致信息超过一分一致的信息。我们在本信中研究赤道分解渠道数量能力的增益如何与所考虑的系统层面相关。我们利用基于无线连接的论据,以证明作为这种频道系列的一个维度功能,可能存在的超增加效应减少。此外,我们证明,在美元-右线-rowloor-infty美元时,离子通道的能力与一致的信息相吻合。我们的结论是,当高维度分解离层的频道的量能力增加量能力与所考虑的系统层面有关。我们利用基于无线约束的参数进行论证,以证明可能的超量效应降低,作为这种频道的维度功能的功能功能功能。此外,我们证明,当美元-右线-线-infty 美元-fty 美元使用时,当出现分解离噪噪噪音时,该频道的一致数据时,并非任何可实现的最高比例。