  In this paper, we present a condition for the zero-error capacity of quantum
channels. To achieve this result we first prove that the eigenvectors (or
eigenstates) common to the Kraus operators representing the quantum channel are
fixed points of the channel. From this fact and assuming that these Kraus
operators have at least two eigenstates in common and also considering that
every quantum channel has at least one fixed point, it is proved that the
zero-error capacity of the quantum channel is positive. Moreover, this
zero-error capacity condition is a lower bound for the zero-error capacity of
the quantum channel. This zero-error capacity condition of quantum channels has
a peculiar feature that it is easy to verify when one knows the Kraus operators
representing the quantum channel.
