Entangled photons – Experimental determination of the correlation function

Alice and Bob can only determine the correlation by comparing their random patterns after the measurement. For that purpose, we compare the corresponding random patterns and substract, for every angle difference (ß−α), the coinciding combinations (White/White, Black/Black), from the non-coinciding combinations (Grey boxes).
The resulting correlation depends upon the angle difference (ß−α). For identical angles, we obtain total correlation, for (ß−α)=90°, anti-correlation. For 45°, the measurement results are uncorrelated.

If we compare the correlation obtained by experimentation (white dots) with the theoretical predictions of quantum physics (red curve), there are still minor deviations occurring after 64 measurements, but, overall, we already recognise a good accordance.
In the actual experiment, approx. 100,000 photons per second are measured. Theory and experiment then match perfectly, constituting the correlation function of |Ω>.

The correlation function describes the connection between Alice’s and Bob’s measurement results. Here, the difference between correlation and information can be seen: We visualise information as chess boards, correlation as the overlay of both chess boards. Correlation emerges without any time delay. However, In order to recognize this correlation, Alice and Bob need to exchange the digital information of their measurement data. This is only possible with a time delay, and not faster than with the speed of light.