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?