  Even though entanglement is very vulnerable to interactions with the
environment, it can be created by purely dissipative processes. Yet, the
attainable degree of entanglement is profoundly limited in the presence of
noise sources. We show that distillation can also be realized dissipatively,
such that a highly entanglement steady state is obtained. The schemes put
forward here display counterintuitive phenomena, such as improved performance
if noise is added to the system. We also show how dissipative distillation can
be employed in a continuous quantum repeater architecture, in which the
resources scale polynomially with the distance.
