The task of determining whether a given quantum channel has positive capacity to transmit quantum information is a fundamental open problem in quantum information theory. In general, the coherent information needs to be computed for an unbounded number of copies of a channel in order to detect a positive value of its quantum capacity. However, in this paper, we show that the coherent information of a $\textit{single copy}$ of a $\textit{randomly selected channel}$ is positive almost surely if the channel's output space is larger than its environment. Hence, in this case, a single copy of the channel typically suffices to determine positivity of its quantum capacity. Put differently, channels with zero coherent information have measure zero in the subset of channels for which the output space is larger than the environment. On the other hand, if the environment is larger than the channel's output space, identical results hold for the channel's complement.

中文翻译：

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量子通道或其补码的相干信息通常是正的

确定给定量子信道是否具有传输量子信息的正容量的任务是量子信息论中的一个基本开放问题。通常，需要为无限数量的信道副本计算相干信息，以便检测其量子容量的正值。然而，在本文中，我们表明如果通道的输出空间大于其环境，则 $\textit{随机选择通道}$ 的 $\textit{single copy}$ 的相干信息几乎肯定是正的。因此，在这种情况下，通道的单个副本通常足以确定其量子容量的积极性。换句话说，具有零相干信息的通道在输出空间大于环境的通道子集中测量为零。另一方面，