  We propose a new measure of the nonclassical distance in the case of Gaussian
states. Let us consider two Gaussian states one of which is fixed and the other
runs through the set of Gaussian classical states. The maximum value of the
fidelity between these two states can be used as a nonclassical distance of the
fixed state to the set of classical states, in the same extent as the Hillery
measure. This measure increases when on the fixed state acts a Gaussian noise
map i.e. the selected state becomes closer to the classical states.
