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 Letter, we show that the coherent information of a single copy of a 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.

翻译：确定特定量子信道是否具有传播量子信息的积极能力的任务在量子信息理论中是一个根本性的开放问题。 一般来说,需要计算一个频道无限制的份数的一致信息,以检测其量子能力的正值。 但是,在本信中,我们表明,如果频道的输出空间大于环境,随机选择的频道的单一副本的一致信息几乎肯定是肯定的。 因此,在这种情况下,频道的单一副本通常足以确定其量子能力的正比性。 换句话说,在输出空间大于环境的频道子集中,无一致信息的频道测量为零。 另一方面,如果环境大于频道的输出空间,频道的补充结果也是一样的。