General formulas for capacity of classical-quantum channels

Coding problems of classical-quantum channels are considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a channel. The channel capacity as well as the characterization of the strong converse property is given just in parallel with the corresponding classical results of Verd\'{u}-Han based on the so-called information-spectrum method. The general results are applied to the stationary memoryless case with or without cost constraint, whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated