  We introduce a scheme to perform dissipation-assisted quantum information
processing in ion traps considering realistic decoherence rates, for example,
due to motional heating. By means of continuous sympathetic cooling, we
overcome the trap heating, and show that the damped vibrational excitations can
still be exploited to mediate coherent interactions as well as collective
dissipative effects. We describe how to control their relative strength
experimentally, allowing for protocols of coherent or dissipative generation of
entanglement. This scheme can be scaled to larger ion registers for coherent or
dissipative many-body quantum simulations.
