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