If you're speaking specifically of this experiment, nowhere in the article does it say that it's using entanglement to do faster-than-light communication. So I don't think there's anything to explain.
If you're asking in general, the very brief summary is this:
(1) In both relativistic and non-relativistic formulations of quantum mechanics, it's possible to prove general no-go theorems which show that measurement of entangled states convey no information whatsoever.
(2) In non-relativistic quantum mechanics, the Schroedinger equation has solutions which can propagate information faster than light. However, those solutions disappear in proper relativistic formulations of quantum mechanics. Physicists regard the non-relativistic solutions as mathematical artifacts: mathematically interesting, but not of any direct physical interest.
(3) People have constructed non-linear variants of quantum mechanics in which it is possible to send information faster-than-light using entanglement. These are toy models - a little like saying "But what if I had a box that could solve the halting problem" in computer science - and, to put it mildly, they are not regarded as promising candidates for physical theories. Not just on account of the FTL problems, either, but also problems like violation of energy conservation, and violations of the second law of thermodynamics. Fun toy theories, but not serious proposals.
Because both photons in the pair must be correlated. From the article:
"The remaining photon from the second path is also reunited with itself from the first path and directed towards a camera, where it is used to build the image, despite having never interacted with the object."
So, they need both the particles together. It doesn't work if one is near Alpha Centauri and cannot be combined with the one on Earth. I'm a complete layman, but this is my understanding of it.
Apparently, the breakthrough here is being able to use different wavelength and intensity of light to interact with an object than that desired for imaging. No information is actually transferred through entanglement.
That's how I read this as well. That said, the medical applications are amazing - they might be able to do MRI-like (or better?!) imaging without the harmful effects!
I'm not a physicist, but as far as I understand, it just doesn't work like that.
Entangled particles start off in a superposition of possible states, when we measure the state of one particle, we can deduce the state of the other particle because we know that the superposition collapses for both particles when the state of either particle is measured, however, no classical information is actually communicated between the particles at the time of measurement.
Just like how the the collapsing wave function in the double-slit experiment appears to "reach back in time" to destroy the interference pattern, a similar effect occurs when the superposition of our entangled particles collapse. Scientists have ruled out the idea that a "hidden variable" secretly stores the true state of the entangled particles prior to measurement, but for the purposes of communicating classical information, this might as well be the case.
Think about it this way.
You create two books with a table - in one column, the time, in another column, a value, either 0 or 1. They are identical, except that the 0s and 1s are switched in both books.
Now you give one of the books to a space traveller, who gets on a rocket that will take him 10 light years away from Earth. You also agree, that once he is there, both you and him will look at your respective books and look at the same time and it's value. So he goes away, and then when the time comes, you open your book, look at the time and read it's value - it's 1, so that means that his book must say 0. Now, there is no "transfer" of information involved - you have not communicated with someone 10 light years away. The information was encoded in the book when it was created, not when you read the information. The same with quantum entanglement - it's already decided when the particle is created,not when you look at it - so it doesn't matter how far the particles are apart, you are just reading pre-defined information.
Edit: no, I am not a physicist either, but I read this explanation somewhere and I think it explains it fairly well.
From a practical perspective: In order to transmit any meaningful data through a quantum-entangled channel, you always need an additional classic channel as well. QE alone cannot transmit any information. The only reason then to use QE for data transmission is that it makes the transmission tamper-proof.
