  Photon subtraction is useful to produce nonclassical states of light
addressed to applications in photonic quantum technologies. After a very
accelerated development, this technique makes possible obtaining either single
photons or optical cats on demand. However, it lacks theoretical formulation
enabling precise predictions for the produced fields. Based on the
representation generated by the two-mode $SU(2)$ coherent states, we introduce
a model of entangled light beams leading to the subtraction of photons in one
of the modes, conditioned to the detection of any photon in the other mode. We
show that photon subtraction does not produce nonclassical fields from
classical fields. It is also derived a compact expression for the output field
from which the calculation of conditional probabilities is straightforward for
any input state. Examples include the analysis of squeezed-vacuum and
odd-squeezed states. We also show that injecting optical cats into a beam
splitter gives rise to entangled states in the Bell representation.
