  We propose a whole family of physical states that yield a violation of the
Bell CHSH inequality arbitrarily close to its maximum value, when using
quadrature phase homodyne detection. This result is based on a new binning
process called root binning, that is used to transform the continuous variables
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.
