Propagation of transverse intensity correlations of a two-photon state

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly correlated photon pairs in an Einstein-Podolsky-Rosen-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anticorrelation, or no correlation, depending on the sum of the orders $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between the theory and experiment.