Amplification of maximally-path-entangled number states

We examine the behavior of a non-Gaussian state like the maximally path-entangled number state commonly known as a N00N state under phase-insensitive amplification. We derive an analytical result for the density matrix of the N00N state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the N00N state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that N00N states are more robust than their Gaussian counterparts.