Homodyning Bell's inequality

We propose to test Bell's inequality through homodyne tomography. The experimental apparatus is mainly composed of a nondegenerate optical parametric amplifier and four photodiodes. The experimental data are gathered through a self-homodyne scheme and are processed by quantum tomography. Our procedure does not introduce supplemen- tary hypotheses (fair sampling assumption), since we do not need to collect auxiliary data to normalize probabilities. Moreover in the proposed experiment, the minimum value of detector quantum efficiency ? is virtually reduced down to ? = .5 (in practice to ? ~ 65 ÷ 70%). The feasibility of the experiment is shown by some numerical results based on Monte-Carlo simulations.