  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.
