If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit nonzero classical information. Here we study how well we can transmit classical information with $N$ depolarizing channels put in superposition of $M$ causal orders via a quantum switch. We calculate the Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with $M$ and it is independent of $N$. For a qubit it never reaches 1 if we are increasing $M$. On the other hand, the classical capacity decreases with the dimension $d$ of the message system. Further, for $N=3$ and 4 we studied the superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by a cyclic permutation subgroup.

中文翻译：

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N完全去极化通道具有不确定因果顺序的经典通信

如果将完全去极化通道的两个相同副本置于其可能因果顺序的叠加中，则它们可以传输非零经典信息。在这里，我们研究我们可以如何很好地传输经典信息$N$ 去极化通道叠加 $米$通过量子开关的因果顺序。如果叠加仅使用通道的循环排列，我们计算 Holevo 量，并发现它随着$米$ 并且它独立于 $N$. 对于一个量子比特，如果我们增加，它永远不会达到 1$米$. 另一方面，经典容量随着维度的增加而减少$d$的消息系统。此外，对于$N=3$ 和 4 我们研究了所有因果顺序的叠加和属于由循环置换子群创建的不同陪集的均匀叠加因果顺序。