A new upper bound for the quantum capacity of the $d$-dimensional depolarizing channels is presented. Our derivation makes use of a flagged extension of the map where the receiver obtains a copy of a state ${\sigma }_0$ whenever the messages are transmitted without errors, and a copy of a state ${\sigma }_1$, when instead the original state gets fully depolarized. By varying the overlap between the flag states, the resulting transformation nicely interpolates between the depolarizing map (when ${\sigma }_0={\sigma }_1$), and the $d$-dimensional erasure channel (when ${\sigma }_0$ and ${\sigma }_1$ have orthogonal support). We find sufficient conditions for degradability of the flagged channel, which let us calculate its quantum capacity in a suitable parameter region. From this last result we get the upper bound for the depolarizing channel, which by a direct comparison appears to be tighter than previous available results for $d>2$, and for $d=2$ it is tighter in an intermediate regime of noise. In particular, in the limit of large $d$ values, our findings present a previously unnoticed $\mathcal{O}(1)$ correction.

中文翻译：

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消极通道量子容量上的量子标志和新界。

量子能的新上限 $d$提出了三维去极化通道。我们的推导利用地图的标记扩展名，在该扩展名中，接收者获得状态的副本${\sigma }_0$ 消息无误地传输，以及状态的副本 ${\sigma }_{\mathrm{1个}}$，相反，原始状态会完全消极。通过更改标记状态之间的重叠，可以很好地在去极化图之间插值（当${\sigma }_0={\sigma }_{\mathrm{1个}}$），以及 $d$尺寸擦除通道（当 ${\sigma }_0$ 和 ${\sigma }_{\mathrm{1个}}$具有正交支持）。我们找到了标记通道可降解性的充分条件，这使我们可以在合适的参数区域中计算其量子容量。从最后的结果中，我们获得去极化通道的上限，通过直接比较，该上限似乎比以前的可用结果更严格。$d>2$和 $d=2$在中间噪声状态下，它会更严格。特别是在极限大$d$ 值，我们的发现提出了以前未曾注意到的 $\mathcal{Ø}（\mathrm{1个}）$ 更正。