  We consider wave transport phenomena in a $\mathcal{PT}$-symmetric extension
of the periodically-kicked quantum rotator model and reveal that dynamical
localization assists the unbroken $\mathcal{PT}$ phase. In the delocalized
(quantum resonance) regime, $\mathcal{PT}$ symmetry is always in the broken
phase and ratchet acceleration arises as a signature of unidirectional
non-Hermitian transport. An optical implementation of the periodically-kicked
$\mathcal{PT}$-symmetric Hamiltonian, based on transverse beam propagation in a
passive optical resonator with combined phase and loss gratings, is suggested
to visualize acceleration modes in fractional Talbot cavities.
