Maximal violation of Bell's inequality and atomic cascade photons
Abstract
Description
A correlation inequality is derived from local realism and a supplementary assumption. This inequality is violated by a factor of 1.5 in the case of real experiments, whereas previous inequalities such as Clauser-Horne-Shimony-Holt inequality of 1969 and Clauser-Horne inequality of 1974 are violated by a factor of $\sqrt 2$. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, the present inequality can be used to test locality very simply because it requires the measurements of only two detection probabilities. In contrast, Clauser-Horne inequality requires the measurements of five detection probabilities.
LaTeX file, 18 pages, no figures. The paper has been significantly modified. It is shown that the in the case of ideal experiments, the inequality derived in this paper is equivalent to Bell's original inequality of 1965 which, as is well known, is violated by a factor of 1.5. The crucial point is that even in the case of real experiments where polarizers and detectors are non-ideal, the present inequality is violated by a factor of 1.5, whereas previous inequalities such as CHSH inequality of 1969 and CH inequality of 1974 are violated by a factor of $\sqrt 2$
LaTeX file, 18 pages, no figures. The paper has been significantly modified. It is shown that the in the case of ideal experiments, the inequality derived in this paper is equivalent to Bell's original inequality of 1965 which, as is well known, is violated by a factor of 1.5. The crucial point is that even in the case of real experiments where polarizers and detectors are non-ideal, the present inequality is violated by a factor of 1.5, whereas previous inequalities such as CHSH inequality of 1969 and CH inequality of 1974 are violated by a factor of $\sqrt 2$