# Common variables and correlation phase shift

Considering that the so-called hidden common variables are uniformly distributed over the numerical experiment and that they are angles on a circle, when these variables have a constant difference of N° between the arms, we observe a phase shift of the correlations by differences of angles of N°.

In order, 90 °, 45 ° and 23 °. The numerical curve, called sioux on the graph, is in green and the cos² in violet.

In the 3 cases, for the angles difference -80 ° , how do Alice and Bob to correlate as much? Yet, everything is random, there is just the sharing of a common variable that is used with a constant shift.

If we apply a small shift over the variables 180° amplitude, for example from 2° to 10°, the curve shape is still preserved with a small degradation. An alternative shift is to make noise by adding a randomly positive or negative value to one of the two arms.

Beyond 20° (on the left), the correlations are everywhere around 50%. The information is insufficient to distinguish the curve from one of correlations between idiot non-entangled photons (right) which should be flatter after a greater number of trials.