  We provide a detailed analysis of the recently proposed setup for a
loophole-free test of Bell inequality using conditionally generated
non-Gaussian states of light and balanced homodyning. In the proposed scheme, a
two-mode squeezed vacuum state is de-gaussified by subtracting a single photon
from each mode with the use of an unbalanced beam splitter and a standard
low-efficiency single-photon detector. We thoroughly discuss the dependence of
the achievable Bell violation on the various relevant experimental parameters
such as the detector efficiencies, the electronic noise and the mixedness of
the initial Gaussian state. We also consider several alternative schemes
involving squeezed states, linear optical elements, conditional photon
subtraction and homodyne detection.
