There are "pure quantum evolution" processes (those described by unitary evolution of ket vector), such as atom sitting forever in its ground state or being in

There are "pure quantum evolution" processes (those described by unitary evolution of ket vector), such as atom sitting forever in its ground state or being in a superposition of different Hamiltonian eigenstates. Those are time-reversible. There are other processes which are not of such kind. Some people don't want to call those quantum processes, but they sure do have a prominent place in QM textbooks. For example spontaneous emission of light from an excited atom or radioactive decay of uranium atomic nucleus. Description of these processes isn't reducible to unitary evolution, instead irreversibility is assumed by employing the golden rule.