  Using the quantum analog of conditional probability and classical Bayes
theorem we discuss some aspects of quantum-classical and classical-classical
channels in connection to the recent paper J. Korbicz, P. Horodecki, and R.
Horodecki, "Quantum-correlation breaking channels, broadcasting scenarios, and
finite Markov chains". Applying the quantum analog of Perron-Frobenius theorem
we generalize the result of Korbicz et. al. on full and spectrum broadcasting
from quantum-classical channels to arbitrary channels.
