Loophole-free test of quantum nonlocality using high-efficiency homodyne detectors -: art. no. 022105

We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality violation 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 tolerance of the achievable Bell violation in the various experimentally relevant parameters such as the detector efficiencies, the electronic noise, the mixedness of the initial Gaussian state, and the probability of false triggers. We also consider several alternative schemes involving squeezed states, linear optical elements, conditional photon subtraction, and homodyne detection.