In short I think this will turn out to be a pivotal finding for melding quantum theory with GR. Quite exciting and possibly prize winning work !

In long They are discussing the use of quantum field theory methods - calculations illustrated by Feynman diagrams - which have some surprising results, that being the 'quantum' terms vanishing and only a 'classical' ( no Planck's constant ) terms remaining. But this is not arbitrary, indeed it 'falls out' of the analysis :

"The researchers had stumbled upon an unexpected pattern in the amplitude haystack. It showed that they didn’t need an infinite number of amplitudes to study classical waves. Instead, they could stop at the five-point amplitude — which involves only a single particle of radiation."

"The expectation is that quantum field theory does describe classical physics ........ It turns out that it is in this way that it does it, by having zero uncertainty in some states." 

If this bears scrutiny then it would solve a long standing dilemma ie. can QM and GR be applied simultaneously ?

Cheers, Mike.

( edit ) BTW you can have zero uncertainty for some quantity in a QM state, provided that the 'conjugate variable' for that quantity has maximum/infinite uncertainty. Thus Heisenberg's Principle is preserved. Naturally whether such states actually exist is a matter of measurement to validate ( or not ).

( edit ) On reflection, something akin to this must be true ie. there is some scale/range at which both QM ( in the micro ) and GR ( in the macro ) agree. There is a mathematical subtlety here though. This process of combining amplitudes to some arbitrary degree of 'finesse', I'm guessing, is going to rely on the grouping of terms in a series. In theory this is an infinite series, and historically there has been much discussion about whether one can legitimately re-arrange the order of terms within. For finite sums we are used to the order of addition not mattering much - your grocery bill will add up to the same total regardless of the sequence of operations - provided you neither miss nor multiply count anything. However an infinite sum is strictly a limit approached by successively 'closer' finite sums. There's the rub though : is the convergence of said series affected by term grouping, and if so then do the limits agree anyhow ? So I reckon they have done some term grouping that causes some given order and all higher terms to mutually cancel, leaving a relatively small ( ie. finite ) handful that matter. Watch this space ..... ;-)

( edit ) If I read this correctly, it ought also say something about the centre of a black hole. Maybe it's not an infinitely dense singularity after all : very massive & very dense to be sure, but finitely so.

( late edit ) Second thought : If not cancelling terms, then another way to be rid of quantum terms is to let Planck's constant tend to zero in the relevant expressions ..... yielding the limiting case of the classical world with no uncertainty principle. Yeah ... probably and/or that.