  We consider the time evolution of an open quantum system subject to a
sequence of random quantum channels with a stationary distribution. This
incorporates disorder into the repeated interactions (or, quantum collision
models) approach to understanding open quantum dynamics. In the literature,
various specific models of disorder in repeated interaction models have been
considered, including the cases where the sequence of quantum channels form
either i.i.d. or Markovian stochastic processes. In the present paper we
consider the general structure of such models without any specific assumptions
on the probability distribution, aside from stationarity (i.e.,
time-translation invariance). In particular, arbitrarily strong correlations
between time steps are allowed. In 2021, Movassagh and Schenker (MS) introduced
a unified framework in which one may study such randomized quantum dynamics,
and, under a key strong decoherence assumption proved an ergodic theorem for a
large class of physically relevant examples. Here, we recognize the decoherence
assumption of MS as a kind of irreducibility and develop a reducibility theory
for general stationary random repeated interaction models without this
condition. Within this framework, we establish ergodic theorems extending of
those obtained by MS to the general stationary setting.
