Ancilla-assisted measurement of photonic spatial correlations and entanglement

We report an experiment in which the moments of spatial coordinates are measured in down-converted photons 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 acts as an ancilla system. Information about the spatial correlations is obtained via measurements on the ancilla qubit. Among other applications, this new method provides a more efficient technique to identify continuous variable entanglement.