We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of some of these low-noise channels such as the depolarizing channel. We also show that both capacities are equal to the single-letter coherent information of the channel, again to leading orders. We thus find that, in the low noise regime, super-additivity and degenerate codes have negligible benefit for the quantum capacity, and shielding does not improve the private capacity beyond the quantum capacity, in stark contrast to the situation when noisier channels are considered.

中文翻译：

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低噪声通道的量子和私有容量

我们确定低噪声量子通道的量子容量和私有容量，以使其在距离理想通道的距离内处于领先地位。确定这些低噪声通道（例如去极化通道）的容量一直是二十多年来的一个开放问题。我们还表明，两种容量均等于渠道的单字母相干信息，再次等于领先订单。因此，我们发现，在低噪声状态下，超可加性和简并码对量子容量的好处微​​不足道，而屏蔽功能并不能改善超出量子容量的私有容量，这与考虑噪声信道的情况形成了鲜明的对比。