"Delayed choice" quantum imaging experiment - why wouldn't it work? I was just reading a Nature news article (Entangled photons make a picture from a paradox, 27 August 2014) about a way to form an image of an object out of photons that have not interacted with the object, but which are entangled with photons that have. The article has a photograph of the image, which is of a cardboard cutout of a cat.
If I understand correctly, the technique is that 


*

*a photon beam is split, e.g. via a semi-silvered mirror, resulting in two beams, call them A and B; 

*in each beam there is some device that turns each photon into two entangled photons. At this point there are four beams, call them A1, B1, A2 and B2. 

*The photons in beam A1 interact with the cardboard cat

*The photons in beam A1 are allowed to interact with the photons from beam B1 in some fashion, and then discarded

*The photons in beams B2 and A2 (neither of which has interacted with a photon that's interacted with the object) are combined somehow and used to produce the image.


This is pretty neat - the article talks about using to image an object with very low-energy photons, while still being able to make an image on a screen using high-energy ones.
However, the following occurred to me while reading about it: presumably, as with all experiments of this kind, it shouldn't in principle make any difference if we change the length of the beams. What would happen if we keep the length of beams A2 and B2 short, but we make beams A1 and B1 really long, say a few light hours?
In this thought experiment the cardboard cat, along with the device for combining the photons from beams A1 and B1, is on Pluto, and the rest of the equipment is in a lab on Earth. It seems as if it should work just as well in this case as it does with everything in the same lab. But now we're seeing the image of the cat five hours before the photons interact with it - and by swapping the cat out for a different object, someone on Pluto could send us a message from the future.
Presumably this can't really work, since it would be possible to construct a paradox if it did. But where is the issue? Have I misunderstood something about the setup (entirely possible since I'm getting this from the news article rather than the actual paper), or is there some fundamental reason why it would stop working if the A1/B1 beam length was much longer than the A2/B2 one?
This seems similar to delayed choice quantum eraser experiments. However (if I remember correctly from looking into them years ago) in those experiments you have to combine all the beams back again to make the image in the end, so there's no way to construct a paradox.  In this case the Nature news article seems quite clear that the photons are thrown away after interacting with the cardboard cat, and the image is produced only from those that haven't - this seems to be a major difference.
 A: 
a Nature news article (Entangled photons make a picture from a paradox, 27 August 2014)

The news article refers to the article "Quantum imaging with undetected photons", Gabriela Barreto Lemos et al. & Anton Zeilinger, Nature 512, 409–412, (28 August 2014).
There is a corresponding arxiv article (1401.4318) with the same figures  available.

a way to form an image of an object out of photons that have not interacted with the object, but which are entangled with photons that have [...]
Have I misunderstood something about the setup [...] ?

A key element of the schematic of the experiment (i.e. Figure 1) is that the photons which have interacted with the object (marked red) are subsequently directed to a nonlinear crystal NL2 where in turn a photon originates (marked yellow) which eventually contributes to forming the image.
(I'd say that the description of the news article about "certain pairs of photons being recombined" is a bit misleading on this point; and there's apparently no mentioning of "recombination" in the arxiv article.)
The schematic of the experiment requires that "an effective light beam" runs, through several optical elements, from the object to the "screen"; even though there are different photons (marked red vs. marked yellow) contributing to different segments of that "effective light beam".
In other words: any event at which "the image is made on the screen" is within, or at least on, the future light cone of the corresponding event at the "the object had been illuminated".
And this requirement stands in the way of paradoxial implementations.

in [other] experiments you have to combine all the beams back again to make the image in the end, so there's no way to construct a paradox.

For the experiment considered here it is also true that the two (yellow) signal pulses must be coincident at the final (combining) beam splitter BS2; after corresponding two (green) laser pulses had been generated (in coincidence) at beam splitter BS1.
But here the passages through the nonlinear crystals (NL1 and NL2) effectively allows photons to be substituted ("yellow for red") along the way. Consequently, the frequency of photons (red) illuminating the object and the frequency of photons (yellow) which make the image may be different from each other; which may be used to "practical/technical" advantage.
A: I think the experiment you are referring to is a little smarter than your description of it. It is not a "simple" quantum entanglement imaging experiment, but it actually uses non-linear crystals to change the wavelengths of the photons along the two light paths. This eliminates the usual explanation, that photons along both arms of the experiment are not distinguishable. I could not read the actual article, yet, but based on the abstract, I believe that the authors are mis-interpreting the meaning of their experiment by treating their non-linear dividers as classical objects. Instead, I think, one needs to include the quantum state of the dividers in the entire quantum state of the experiment. This means, that this experiment only works for beams that do not exceed the coherence time of the dividers. In your case, the experiment would fail, if one would set it up with 5 hour light times, which far exceeds the time that the dividers can "remember" the photons they were exposed to. 
Alternatively, imagine the experiment augmented with a strong bleaching laser at each of these dividers, which would reset their quantum state while the actual imaging photons are moving down both arms of the experiment. Bleaching any one of the non-linear dividers would be similar to removing a mirror from a simple (single wavelength) entanglement experiment, which would destroy the image as well. All in all it's a very smart experiment, but it really doesn't tell us anything about QM that we didn't know, already. At most it challenges us to analyze the system properly (including the states of the atoms in the dividers, which is not necessary for the similar experiment with ordinary mirrors). 
