Nonlinear dissipation can combat linear loss

For nonclassical state generation, we demonstrate the possibility to compensate effects of strong linear loss by engineered nonlinear dissipation. We show that it is always possible to construct such a dissipative gadget that, for a certain class of initial states, the desired nonclassical state can be attained within a particular time interval with an arbitrary precision. Further we demonstrate that an arbitrarily large linear loss can still be compensated by a sufficiently strong coherent or even thermal driving, thus obtaining strongly nonclassical (in particular, sub-Poissonian) stationary mixed states.