Some formulas

– \(\vartheta\) is the random rotation
– \(a_i\) is a picked value around a shared variable. The randomizer must give an uniform repartition.
– \(n\) is an ad hoc integer parameter between \(5\) and \(\infty\)

Probability to render 1 at each step in the polarizer :
\(p_1 = \prod_{i=1}^{n}{ cos^2(a_i-\vartheta )} ;\)

Probability to render 0 at each step in the polarizer :
\(p_2 = \prod_{i=1}^{n}{ sin^2(a_i-\vartheta )} ;\)

Probability to fail and to try again :
\(p_0 = 1.0 – p_1 – p_2 ;\)

Final probability to render 1 after the whole polarization attempt :

\(P_1 = \frac{p_1 p_0^{\pi^{n-2}}}{ \left(p_1+p_2\right)} ;\)

Final probability to render -1 after the whole polarization attempt :

\(P_{-1} = \frac{p_2 p_0^{\pi^{n-2}}}{ \left(p_1+p_2\right)} ;\)

Final probability to render 0 for an undetected particle after the whole polarization attempt :
\(P_0 = 1.0 -P_1-P_{-1} ;\)

This hack describes correctly the experiments outcomes.

 

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