  The driven-dissipative Bose-Hubbard model can be experimentally realized with
either negative or positive onsite detunings, inter-site hopping energies, and
onsite interaction energies. Here we use one-dimensional matrix product density
operators to perform a fully quantum investigation of the dependence of the
non-equilibrium steady states of this model on the signs of these parameters.
Due to a symmetry in the Lindblad master equation, we find that simultaneously
changing the sign of the interaction energies, hopping energies, and chemical
potentials leaves the local boson number distribution and inter-site number
correlations invariant, and the steady-state complex conjugated. This shows
that all driven-dissipative phenomena of interacting bosons described by the
Lindblad master equation, such as "fermionization" and "superbunching", can
equivalently occur with attractive or repulsive interactions.
