it is actually pretty spooky setup. May be there is a Nobel Prize lurking there, yet looking at the Figure 2 of their arxiv paper http://arxiv.org/ftp/arxiv/papers/1401/1401.4318.pdf

one can't wonder why for example the beam L4'-L5 isn't filtered out - if this beam does carry information about the image then we would have FTL communication possible.

Another question is why L3-L3' red beam - the image info carrying beam - is fed into NL2 crystal thus providing a chance to physically affect formation of NL2-D5-L6 yellow beam, ie. to exchange information. Some of the red beam photons entering NL2 would be consumed and re-emitted by the NL2 crystal's atoms (and the location of these atoms will be affected by the red beam internal density ie. by the image of the object "O") and thus would physically affect the yellow beam generation, i.e. passing some image info into the yellow beam. Thus no entanglement or other "spooky" QM features necessary for the NL2-D5-L6 yellow beam to become carrying some image info.