In the exploration of the limits of the description of the physical world offered by quantum mechanics, one of the outstanding questions is why QT is exactly as nonlocal [1] and contextual [2] as it is. 
One of the possible explanation is based on the concept of exclusivity (E) principle:
the sum of the probabilities of any set of pairwise exclusive events cannot exceed 1.

In order to prove if the E principle explains the features of quantum theory it is important to asses experimentally the extremal value for 
quantum violation of the Bell-CHSH inequality [1, 2] and quantum correlations in other scenarios.
We used the standard setup for the demonstration of the violation of the Bell inequality, specifically the CH one, and optimized the experimental parameter and the collected statistics in in order to maximize the violation and reduce the uncertainty on the obtained value.

Comparing our value with the other presented in the literature, we can establish a lower bound on the maximum attainable violation  that represents an improvement of (one? two?) order of magnitude with the values previously reported.