 For the maximally entangled states we have been considering, in the idealized case of perfect detection efficiency, inequality (25) is maximally violated by the quantum predictions for the same settings considered above for violation of the CHSH inequality. However, for non-ideal experiments, the quantum predictions satisfy the inequality unless detector efficiency is high, considerably higher than that of any experiment that had been performed up until the time that CH were writing. For that reason, CH introduced a new auxiliary assumption, called the no-enhancement assumption: for any value of \(\lambda\), and any setting of an analyzer, the probability of detection with the analyzer present is no higher than the probability of detection with the analyzer removed. Let \(p^1_{\infty}\) and \(p^2_{\infty}\) be the probabilities of detection of particles 1 and 2 when their respective analyzers have been removed. This assumption gives rise to what may be called the second CH inequality: