  We report an experiment in which the moments of spatial coordinates of
down-converted photons are measured directly, without having to reconstruct any
marginal probability distributions. We use a spatial light modulator to couple
the spatial degrees of freedom and the polarization of the fields, which act as
ancilla systems. Information about the spatial correlations is obtained via
measurements on the ancilla qubits. Among other applications, this new method
provides a more efficient technique to identify continuous variable
entanglement.
