The first step after alignment was to set the apparatus to the desired state. This was done by setting the polarizations in the state’s anti-correlated position and adjusting the SPDC and alignment crystal to minimize the coincidence rate. To check the quality of the entangled state, the visibility was measured, which is given by the equation [4] \[V=\frac{C_{max}-C_{min}}{C_{max}+C_{min}}\]
The visibility was \(V_{\psi_+}=0.910 \pm 0.015\) and \(V_{\psi_-}=0.889\), which was propagated using a Poisson distribution for the counts [5]. A level this high indicates a high degree of entanglement, and so it was appropriate to continue with the experiment.
Once this was done, the coincidence rate was taken for the 16 different required measurements by rotating the polarizing filters. The experimental results are shown in [fig:Table 1].
The error for \(E(a,b)\) was calculated through standard error propagation and by using \(\delta C(a,b)=\sqrt{C(a,b)}\), which is
\[\textstyle{ \Delta E(a,b) = 2\sqrt{\frac{(N(a,b)+N(a_\perp,b_\perp))(N(a_\perp,b)+N(a,b_\perp))}{(N(a,b)+N(a_\perp,b_\perp)+N(a_\perp,b)+N(a,b_\perp))^3}} }\]
The error for \(S\) was propagated using the same standard method. The errors for both \(\psi_+\) and \(\psi_-\) are very small, giving a sigma of 14, which is high enough to conclude our experiment as successful.