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I understand that experimental results from Bell test experiments have shown that measured correlation is a cosine function of the angle between the detectors. What I am struggling to grasp is why classical/local variable theories wouldn't allow this, and why a quantum mechanical/non-local theory would.

Any explanation is appreciated!

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    $\begingroup$ You've already read the kind of shortened, condensed and simplified version you're asking for and it didn't help because the idea is subtle. Thus, my usual comment to the effect that you're not going to get it until you do the math for yourself. $\endgroup$ – dmckee --- ex-moderator kitten Jan 31 '16 at 20:24
  • $\begingroup$ First, modified Malus law may reduces the differences with QM. Next, Classical mechanics , even with this modification , is unable to reproduce exactly the predictions of QM while QM-non-localists experimenters claim that they proved the theory. At the same time, if the theory is proved , we must see quantum cryptography running on all the clouds , banks, etc. There is not only one announcement of such implementation. $\endgroup$ – user46925 Jan 31 '16 at 20:28
  • $\begingroup$ "if the theory is proved , we must see quantum cryptography running on all the clouds , banks, etc" Er ... doing it in the lab and commercializing are very different things. You overstate your case. $\endgroup$ – dmckee --- ex-moderator kitten Jan 31 '16 at 20:48
  • $\begingroup$ @dmckee : If you followed the informations on the subject, you must know that commercial announcements had been made first by the physicists themselves. Elections, contestation and next nothing ... It's not common to express such argument but , originally , it wasn't the mine. $\endgroup$ – user46925 Jan 31 '16 at 20:55
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In classical physics, a system can be described by a set of numbers whose values can all be measured using a single instance of that system. In quantum mechanics, a system is characterised by the values of observables where those values are represented by Hermitian matrices. To describe how information is transferred between quantum systems you have to describe the ways in which the observables of one system depend on those of another.

In general, an observable does not represent just a single valued measurable quantity changing over time. Rather, it represents a more complex structure that involves multiple different versions of that quantity interfering with one another. And if there are going to be multiple versions of each system, then any given system has to carry information about how a particular version of that system will interact with a particular version of another system. In general, you can't get that sort of information by measuring just one system and for that reason it is called locally inaccessible information. An explanation of how locally inaccessible information gives rise to EPR correlations, teleportation etc by entirely local interactions is given here:

http://arxiv.org/abs/quant-ph/9906007.

See also

http://arxiv.org/abs/1109.6223.

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