No-enhancement hypothesis

In deriving the BCHSH inequality in the forms (23) and (25) which are applicable in real experimental situations, it was necessary to assume 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. This assumption is known as the no-enhancement hypothesis and was first stated by Clauser, Home, Shimony, and Holt " in the following form If a pair of photons emerges from the polarizers, the probability of their joint detection is independent of the orientations a and b of the polarizers axes. Subsequently, Clauser and Horae stated the hypothesis in the more general form For every atomic emission, the probability of a count with a polarizer in place is less than or equal to the probability with the polarizer removed. 

However, the low efficiency of the photomultipliers used in all these experiments leaves open the possibility that the results could be explained in terms of local realistic theories if the no-enhancement hypothesis is not made. Consequently, no experiment to date can be considered to have provided grounds for a completely unequivocal rejection of such theories, and, indeed, if such an assumption is not made, it has been shown by several authors that it is possible to explain all existing experimental results in local realistic terms. Thus it seems likely that, in future, experimental work will be carried out either in situations where it is not necessary to make the no-enhancement hypothesis, for example in experiments of the type suggested by Lo and Shimony or Selleri, or in situations where the no-enhancement hypothesis can be subjected to direct experimental test, for example in experiments of the type suggested by Garuccio and Selleri. ... 

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