Measuring phase of photon should always be random while checking CHSH inequality, but i can't explain this: http://qudev.ethz.ch/content/courses/QSIT08/pdfs/Rowe01.pdf (the most clear experiment i found):

The experiment is repeated Ntot 20;000 times at each of the four sets of phases

If phase was choosed randomly and independent on every side - how is it possible to receive so clear and constant number of repetitions for every phase combination?

  • if they choose it randomly for every photon - there must be something like 19899 + 20001 + 19888 + 19999
  • if they choose it randomly 4 times: it's also impossible to try all combinations (ab, ab', a'b, a'b') - because sometimes randomizers will just give something like: ab', ab' a'b, a'b'. The only way to always choose polarization with 4 different combos - is pickup random number from 1 to 4 - which is actually will cause correlation between sides - so i hope it's not what they did. Ignoring some experiments will cause same effect.


Each modulator is controlled by amplification from a very rapid generator, which randomly causes one of two rotations of the polarization of the traversing photon.


It seems to be impossible to choose phase randomly with so constant number of choosen combinations (just try to do it with two coins) without communication between sides, but maybe i'm not taking in account something?


The paper you point to describes the experimental test by Rowe et al., in Wineland’s group in 2001. This experiment was performed in an ion trap, where Alice and Bob are separated by 3 µm, and therefore it is impossible in practice to close the locality loophole. As they say in the methods section,

even though all known interactions would cause negligible correlations in the measurement outcomes, the ion separation is not large enough to eliminate the lightcone loophole.

Since it did not try to close this loophole, they did not bother to randomly chose the phase, because the only role of this random choice is to close this loophole, hence the round numbers. In experiments closing the locality loophole, the numbers fluctuate statistically as you describe.

The interest of this experiment is the (separate) closing of the detection loophole. While it is possible to imagine LHV theories which use the locality loophole in this experiment while using the detection loophole for photon experiments, they would need to be very contrived.

And now (2014), 13 years later, no experiment has yet simultaneously closed the detection and the locality loophole, but several groups are working on it.


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