Maximal violation of Bell inequalities using continuous-variable measurements

We propose a whole family of physical states that yield a maximal violation of Bell inequalities, when using quadrature-phase homodyne detection. This result is based on a binning process called root binning, that is used to transform the continuous-variable measurements into binary results needed for the tests of quantum mechanics versus local realistic theories. A physical process in order to produce such states is also suggested. The use of high-efficiency spacelike separated homodyne detections with these states and this binning process would result in a conclusive loophole-free test of quantum mechanics.