  Stochastic exclusion processes play an integral role in the physics of
non-equilibrium statistical mechanics. These models are Markovian processes,
described by a classical master equation. In this paper a quantum mechanical
version of a stochastic hopping process in one dimension is formulated in terms
of a quantum master equation. This allows the investigation of coherent and
stochastic evolution in the same formal framework. The focus lies on the
non-equilibrium steady state. Two stochastic model systems are considered, the
totally asymmetric exclusion process and the fully symmetric exclusion process.
The steady state transport properties of these models is compared to the case
with additional coherent evolution, generated by the $XX$-Hamiltonian.
