  We address conditional de-Gaussification of continuous variable states by
inconclusive photon subtraction (IPS) and review in details its application to
bipartite twin-beam state of radiation. The IPS map in the Fock basis has been
derived, as well as its counterpart in the phase-space. Teleportation assisted
by IPS states is analyzed and the corresponding fidelity evaluated as a
function of the involved parameters. Nonlocality of IPS states is investigated
by means of different tests including displaced parity, homodyne detection,
pseudospin, and displaced on/off photodetection. Dissipation and thermal noise
are taken into account, as well as non unit quantum efficiency in the detection
stage. We show that the IPS process, for a suitable choice of the involved
parameters, improves teleportation fidelity and enhances nonlocal properties.
