Generation of spatial antibunching with free-propagating twin beams. D. Caetano and P. Souto Ribeiro in Phys. Rev. A 68:043806 (2003).  What the paper says!?

We meet Bialynicka-Birula et al. again (what do they do?)

How they cite Nogueira et al.:

Recently, Nogueira, Walborn, Pádua, and Monken⁷ have proposed and implemented a spatial version of the photon antibunching where photons tend to propagate separately with respect to the transverse propagation plane. They have used twin photons from the parametric down-conversion and in their experiment, the final state is prepared by propagation through special double slits, leading to a light beam in which photons seem to repel each other in space.

Here, instead:

In this work, we propose and implement an experimental scheme for obtaining spatial antibunching with free-propagating beams.

By "free-propagating beams" they mean they don't throw away part of the beam by diffraction, as was the case in the earlier paper by Nogueira et al., but Nogueira et al. later upgraded to also use "propagating beams". In this later paper, these authors concede that in their previous work, «the two photons were in a singlet polarization state after the birefringent double slit, but they did not constitute a beam.»

The difference between the two in the words of the authors:

There are two important differences between this scheme and the one implemented in Ref. 关7兴. There, the modulation in the coincidence distribution comes from the interference due to the propagation through a double slit. Here, it comes from the state preparation through the pump beam angular spectrum. Another difference is that in Ref. 关7兴 a quarterwave plate is placed in front of each slit with orthogonal fast axis to introduce a phase shift in the coincidence interference fringe. Here, a Dove prism is used for inverting the transverse coordinate of the wave front of one of the twin beams. Because our method acts in the state preparation, and the propagation through the Dove prism is almost lossless, the amount of the spatially antibunched photons is larger than in Ref. 关7兴.

Clear physical description of CSI violation:

The inequality in Eq. 共1兲 would be violated whenever the coincidence-counting rate for displaced 共in the transverse detection plane兲 detectors is bigger than that for aligned ones. According to previous works 关8兴,

This I don't understand:

The violation of the inequality only results in the spatial photon antibunching if the light beam is homogeneous.

They say that one can violate the CSI but "the violation of the in- equality in Eq. 共1兲, does not imply spatial antibunching."