  The non-Gaussian operations effected by adding or subtracting a photon on the
entangled optical beams emerging from a parametric down-conversion process have
been suggested to enhance entanglement. Heralded photon addition or subtraction
is, as a matter of fact, at the heart of continuous-variable entanglement
distillation. The use of such processes has recently been experimentally
demonstrated in the context of the generation of optical coherent-state
superpositions or the verification of the canonical commutation relations.
Here, we carry out a systematic study of the effect of local photon additions
or subtractions on a two-mode squeezed vacuum state, showing that the
entanglement generally increases with the number of such operations. This is
analytically proven when additions or subtractions are restricted to one mode
only, while we observe that the highest entanglement is achieved when these
operations are equally shared between the two modes. We also note that adding
photons typically provides a stronger entanglement enhancement than subtracting
photons, while photon subtraction performs better in terms of energy
efficiency. Furthermore, we analyze the interplay between entanglement and
non-Gaussianity, showing that it is more subtle than previously expected.
