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.