About the correlation function between two vectors and quantum superposition of photons.
For many years, starting 1982 numerous researchers are investigating the so-called quantum entanglement - quantum superposition of polarized photons. The work started by Alain Aspect, who found that the correlation function between the two simultaneously generated photons in a radiative cascade of calcium [1] is not linear, but follows the law Cos(F), where F is the angle between the polarizers. For intensity that would mean Cos²(F) law. This is exactly the law expected for two completely independent by equally polarized photons (Malus Law).
The deviation from Bell's inequality was thought to occur because of the idea (wrong idea) that for classical case the correlation function between the polarization vectors would be linear (that is directly proportional to angle between polarizers). This is not possible because of the mathematical definitions of vectors: according to [2] the correlation function between any vectors (quantum or classical) must be expressed as a function of Cos and Sin and by no means may be simply proportional to angle. In [2] the correlation function between any vectors is to be proved to be Cos(F) (because it is actually simply normalized dot product of two vectors):

Correlation=Cos(a^.b)=(a^.b)/(|a|^.|b|)

In this case either classical or quantum correlation will follow the Cos(F) law (simple Malus law) and no deviation from Bell's inequality is observed. In [1] a simple generation of two equally polarized photons was observed without any quantum superposition between them.
Linear function of an angle is not possible for correlation function because it will have two special points (at 0 and at 90 degrees), where the derivative is discontinuous, which is not possible for correlation function which must be smooth function. Thus the zig-zag correlation function for classical vectors is equally impossible as for quantum vectors, and the presence of Cos(F) is not proof of quantum behavior of the two independent photons in [1].
This does not exclude the possibility of quantum superposition of photons (and action at the distance), simply the present papers are not proof of it.

References.
1.Alain Aspect, Philippe Grangier, Gerard Roger "Experimantal realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell's inequalities"//Physical Review Letters, Vol.49, No 2, p.p.91-94, 1982.
2.Zenon Gniazdowsi "Geometric interpretation of correlation" // Zeszyty Naukowe Warszawsiej Szkoly Informatyki, No 9, Vol.7, 2013 p.p.27-35.