We present a protocol that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. Based on the results of Munro [PRA 1999], the state is near-optimal for Bell-inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes the Gaussian entanglement distillation protocol of Eisert et. al. [Annals of Phys. 2004] and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter, permitting a loophole-free test of Bell inequalities.
@article{arxiv.quant-ph/0504084,
title = {Generating optimal states for a homodyne Bell test},
author = {Sonja Daffer and Peter L. Knight},
journal= {arXiv preprint arXiv:quant-ph/0504084},
year = {2009}
}