A unital completely positive map governing the time evolution of a quantum system is usually called a quantum channel, and it can be represented by a tuple of operators which are then referred to as the Kraus operators of the channel. We look at states of the system whose correlations with respect to the channel have a certain symmetry. Then we show that detailed balance holds if the Kraus operators satisfy a very interesting algebraic relation which plays an important role in the representation theory of any compact quantum group.