  We study the effects of post-selection measurements on both the
non-classicality of the state of a mechanical oscillator and the entanglement
between two mechanical systems that are part of a distributed optomechanical
network. We address the cases of both Gaussian and non-Gaussian measurements,
identifying the values of the parameters for which simple photon-counting and
Geiger-like measurements are effective in distilling a strongly non-classical
mechanical state and enhancing the purely mechanical entanglement between two
elements of the network.
