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Because of the fundamental importance of Bell's theorem, a loophole-freedemonstration of a violation of local realism (LR) is highly desirable. Here,we study violations of LR involving photon pairs. We quantify the experimentalevidence against LR by using measures of statistical strength related to theKullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam,R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)].Specifically, we analyze a test of LR with entangled states created from twoindependent polarized photons passing through a polarizing beam splitter. Wenumerically study the detection efficiency required to achieve a specifiedstatistical strength for the rejection of LR depending on whether photoncounters or detectors are used. Based on our results, we find that a test of LRfree of the detection loophole requires photon counters with efficiencies of atleast 89.71%, or photon detectors with efficiencies of at least 91.11%. Forcomparison, we also perform this analysis with ideal unbalanced Bell states,which are known to allow rejection of LR with detector efficiencies above 2/3.

The statistical strength of experiments to reject local realism with photon pairs and inefficient detectors