Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam, R. D. Gill, and P. D. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. We numerically study the detection efficiency required to achieve a specified statistical strength for the rejection of LR depending on whether photon counters or detectors are used. Based on our results, we find that a test of LR free of the detection loophole requires photon counters with efficiencies of at least
89.71, or photon detectors with efficiencies of at least
91.11. For comparison, we also perform this analysis with ideal unbalanced Bell states, which are known to allow rejection of LR with detector efficiencies above
2/3.
Recently Hardy has exhibited a striking new violation of local realism that occurs in a pair of interferometers that have been interconnected so that knowledge about the path chosen by a particle in one interferometer conveys some information about the path or paths chosen by the particle in the other interferometer. It has been demonstrated that particle annihilation and a two-photon interference effect can be exploited to give rise to this local realism violation. Here we show that in the case of fermion interferometers the Pauli exclusion principle can be exploited to give rise to this effect.