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

TL;DR

This paper evaluates the statistical strength of experiments using photon pairs and inefficient detectors to convincingly reject local realism, emphasizing the required detection efficiencies for loophole-free Bell tests.

Contribution

It introduces a quantitative analysis of statistical evidence against local realism using KL divergence and determines efficiency thresholds for photon counters and detectors.

Findings

Photon counters need at least 89.71% efficiency.

Photon detectors require at least 91.11% efficiency.

Ideal unbalanced Bell states allow LR rejection above 2/3 efficiency.

Abstract

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. Gill and P. 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.