  A simple and efficient method for characterization of multidimensional
Gaussian states is suggested and experimentally demonstrated. Our scheme shows
analogies with tomography of finite dimensional quantum states, with the
covariance matrix playing the role of the density matrix and homodyne detection
providing Stern-Gerlach-like projections. The major difference stems from a
different character of relevant noises: while the statistics of
Stern-Gerlach-like measurements is governed by binomial statistics, the
detection of quadrature variances correspond to chi-square statistics. For
Gaussian and near Gaussian states the suggested method provides, compared to
standard tomography techniques, more stable and reliable reconstructions. In
addition, by putting together reconstruction methods for Gaussian and arbitrary
states, we obtain a tool to detect the non-Gaussian character of optical
signals.
