Zero-error classical capacity of qubit channels cannot be superactivated

It was shown [T.S. Cubitt et al., IEEE Trans. Inform. Theory 57, 8114 (2011)] that there exist quantum channels where a single use cannot transmit classical information perfectly yet two uses can. This phenomenon is called the superactivation of the zero-error classical capacity which does not occur in classical channels. In this paper, it is shown that qubit channels cannot generate the superactivation.