Some thoughts

@AC - the trick with quantum communication is that there are two sorts of polarisation possible - but you can only measure any one of them - the act of measuring the one you choose destroys the information encoded in the other. So Alice randomly chooses which of the two kinds to use for each photon. Bob randomly chooses one or the other to measure. After the photons are sent Alice sends (in clear) to Bob the choices she made. On average Bob will have measured about half of the photon's polarisation the right way - and these can be assembled to make a key - which is used as a one time pad for the actual communication.

If Eve tries to intercept the photons she must also destroy the information in the polarisation - and can also only recover one of the two sorts. So even if she resends a new photon with the measured polarisation, she only has a 50/50 chance of encoding the other form of polarisation correctly. So Bob will get a sudden jump in errors in the link - which is evidence of an eavesdropper.

The paper seems to show a method for cloning the photons with enough fidelity (because it is intrinsically impossible to perfectly clone this is a probability) and assuming that you are able to keep the clones about without measuring them (a none to trivial task) until Alice sends her choice information, and then measure each photon knowing ahead of time which form of polarisation to measure (something Bob cannot do.) You may get enough leverage to get some useful information out of the link without triggering the eavesdropper error threshold.

Not being an optic boffin either I suspect the leverage is in the ability to keep the clones until Alice sends her choices - this doubles the number good measurements Eve gets. The act of cloning must increase the error rate Bob sees (indeed there should be a conservation law in here somewhere), but it looks as if the additional leverage Eve has with this trick means she gets twice as much information out as Bob sees degraded (since Bob sees half of his measurements listed as useless.) Thus it may be that there is enough wiggle room that Eve can get a partial idea of the key without Bob deciding that the error rate is too great, and there is an intruder. A partial key can be enough.

Like I say, I'm not an expert in this - but it seems to be the general idea.