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



Yanbao Zhang, Emanuel H. Knill, Scott C. Glancy


Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism is highly desirable. Here, we study violations of local realism involving photon pairs. We quantify the experimental evidence against local realism by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by W. van Dam, P. Grunwald and R. Gill [IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of local realism (LR) with an entangled state created from two independent polarized photons passing through a polarizing beam splitter. We study the detection efficiency required to achieve a specified statistical strength for the rejection of local realism 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 efficiency at least ~ 89.71 %, or photon detectors with efficiency at least ~ 91.11 %. For higher efficiencies we obtain and display the relationship between statistical strength and efficiency for optimized experimental configurations involving either the above source or an ideal source of unbalanced Bell states, which is known to allow for efficiencies as low as 2/3.
Physical Review A (Atomic, Molecular and Optical Physics)


foundations of quantum mechanics, Bell's inqualities, entanglement, photon pairs, statistical strength, confidence


Zhang, Y. , Knill, E. and Glancy, S. (2010), The statistical strength of experiments to reject local realism with photon pairs and inefficient detectors, Physical Review A (Atomic, Molecular and Optical Physics), [online], (Accessed December 7, 2023)
Created March 18, 2010, Updated February 19, 2017