  Metastability in open system dynamics describes the phenomena of initial
relaxation to longlived metastable states before decaying to the asymptotic
stable states. It has been predicted in continuous-time stochastic dynamics of
both classical and quantum systems. Here we present a general theory of
metastability in discrete-time open quantum dynamics, described by sequential
quantum channels. We focus on a general class of quantum channels on a target
system, induced by an ancilla system with a pure-dephasing coupling to the
target system and under Ramsey sequences. Interesting metastable behaviors are
predicted and numerically demonstrated by decomposing the average dynamics into
stochastic trajectories. Examples and applications are also discussed.
