  We examine the behavior of non-Gaussian states of light under the action of
probabilistic noiseless amplification and attenuation. Surprisingly, we find
that the mean field amplitude may decrease in the process of noiseless
amplification -- or increase in the process of noiseless attenuation, a
counterintuitive effect that Gaussian states cannot exhibit. This striking
phenomenon could be tested with experimentally accessible non-Gaussian states,
such as single-photon added coherent states. We propose an experimental scheme,
which is robust with respect to the major experimental imperfections such as
inefficient single-photon detection and imperfect photon addition. In
particular, we argue that the observation of mean field amplification by
noiseless attenuation should be feasible with current technology.
