A condition for the zero-error capacity of quantum channels

In this paper, it is proved that the eigenvectors (or eigenstates) common to the Kraus operators representing the quantum channel are fixed points of it. From this and assuming that the Kraus operators that represent the quantum channel have at least two eigenstates in common, it is proved that the zero-error capacity of the quantum channel is positive. This error-zero capacity condition is a lower bound for the error-zero capacity of the quantum channel.