2) Now that the author has passed my “what else has the author done?” test, the author also passes the: Is this paper influential test?
3) _ A method of computing many functions simultaneously by using many parallel quantum systems_
“These experiments report that quantum theory does not accept a Leggett type non-local variables interpretation, although some controversy remains around the conclusions and interpretations of the experimental outcomes [8-10]”
Because influential papers are used in other papers (which is how you know they are influential in some sense), often one can find a short practical summary of that paper within a later paper and also see the paper you’re interested in from the perspective of a COLLECTION of SIMILAR papers with similar results.
Such is the case here. This paper is classified with two others.
Here are the three:
 S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. ˇZukowski, M. Aspelmeyer, and A. Zeilinger, Nature (London) ˙446, 871 (2007).
 T. Paterek, A. Fedrizzi, S. Gröblacher, T. Jennewein, M.Zukowski, M. Aspelmeyer, and A. Zeilinger, Phys. Rev. Lett. ˙99, 210406 (2007).
 C. Branciard, A. Ling, N. Gisin, C. Kurtsiefer, A. LamasLinares, and V. Scarani, Phys. Rev. Lett. 99, 210407 (2007).
8 is the paper you see in the OP.
9 by a similar set of authors, is “Experimental Test of Nonlocal Realistic Theories Without the Rotational Symmetry Assumption”
10 by an entirely DIFFERENT set of authors:
“Experimental Falsification of Leggett’s Nonlocal Variable Model”
all tell me: the paper is about falsifying Leggett’s Nonlocal Variable Model. So what is Leggett’s Nonlocal Variable Model?
4) A search for Leggett nonlocal pulls up a Wikipedia article. https://en.wikipedia.org/wiki/Leggett_inequality
This Wikipedia article summarizes all of what I looked at better than I did.
5) Details of the particular experiment had some in-depth news articles at the time:
A TEAM OF PHYSICISTS IN VIENNA HAS DEVISED EXPERIMENTS THAT MAY ANSWER ONE OF THE ENDURING RIDDLES OF SCIENCE: DO WE CREATE THE WORLD JUST BY LOOKING AT IT?
6) My takeaway from the news article:
” The data defied the predictions of Leggett’s model by three orders of magnitude. Though they could never observe it, the polarizations truly did not exist before being measured. For so fundamental a result, Zeilinger and his group needed to test quantum mechanics again. In a room atop the IQOQI building, another PhD student, Alessandro Fedrizzi, recreated the experiment using a laser found in a Blu-ray disk player.
Leggett’s theory was more powerful than Bell’s because it required that light’s polarization be measured not just like the second hand on a clock face, but over an entire sphere. In essence, there were an infinite number of clock faces on which the second hand could point. For the experimenters this meant that they had to account for an infinite number of possible measurement settings. So Zeilinger’s group rederived Leggett’s theory for a finite number of measurements. There were certain directions the polarization would more likely face in quantum mechanics. This test was more stringent. In mid-2007 Fedrizzi found that the new realism model was violated by 80 orders of magnitude; the group was even more assured that quantum mechanics was correct.”