  We develop the `duality approach', that has been extensively studied for
classical models of transport, for quantum systems in contact with a thermal
`Lindbladian' bath. The method provides (a) a mapping of the original model to
a simpler one, containing only a few particles and (b) shows that any dynamic
process of this kind with generic baths may be mapped onto one with equilibrium
baths. We exemplify this through the study of a particular model: the quantum
symmetric exclusion process introduced in [D. Bernard, T. Jin, Phys. Rev. Lett.
123, 080601 (2019)]. As in the classical case, the whole construction becomes
intelligible by considering the dynamical symmetries of the problem.
