The BCHSH Inequality in Experimental Situations

Adoption of the above procedure, however, implicitly assumes that, for each setting of the polarizers, the ensemble of detected pairs is a true representative sample of the ensemble of pairs emitted by the source. 

The above form (19) of the BCHSH inequality applies to the situation where both orthogonal polarization states are detected on each side of the source. However, most experiments that have been carried out only detect the signals that are transmitted directly through the polarizers. One can 

From Eqs. (21) and (22) it follows that the inequality (19) can be rewritten in the form 

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