# Significant-loophole-free test of Bell's theorem with entangled photons

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Referee this paper: arXiv:1511.03190 by Marissa Giustina, Marijn A. M. Versteegh, (show more)

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requested Sep 28, 2017

paper authored Nov 10, 2015 to quant-ph

abstract : Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed $3.74×10^{-31}$, corresponding to an 11.5 standard deviation effect.

In the supplemental material located here :

The angles of the polarizers are

$a1 = 94°4$ , $a2 = 62°4$ , $b1 = -6°5$ , $b2 = 25°5$.

The number of valid trials is $N = 3,502,784,150$

and the relevant counts are

$N_{11} = N_{100°9} = 875,683,790; N_{11}^{++} = N_{100°9}^{++} = 141,439$

$N_{12} = N_{68°9} = 875,518,074; N_{12}^{+0} = N_{68°9}^{+0} = 67,941$

$N_{21} = N_{68°9} = 875,882,007; N_{21}^{0+} = N_{68°9}^{0+} = 58,742$

$N_{22} = N_{38°9} = 875,700,279; N_{22}^{++} = N_{38°9}^{++} = 8,392$

This study is given as free of the fair-sampling assumption. I was wondering how these values are compatible with this declaration.

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