  We show that the magnetization of a single `qubit' spin weakly coupled to an
otherwise isolated disordered spin chain exhibits periodic revivals in the
localized regime, and retains an imprint of its initial magnetization at
infinite time. We demonstrate that the revival rate is strongly suppressed upon
adding interactions after a time scale corresponding to the onset of the
dephasing that distinguishes many-body localized phases from Anderson
insulators. In contrast, the ergodic phase acts as a bath for the qubit, with
no revivals visible on the time scales studied. The suppression of quantum
revivals of local observables provides a quantitative, experimentally
observable alternative to entanglement growth as a measure of the `non-ergodic
but dephasing' nature of many-body localized systems.
