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arXiv:1506.02712 · Physical Review Letters

Generation of Fresh and Pure Random Numbers for Loophole-Free Bell Tests

Carlos Abellán, Waldimar Amaya, Daniel Mitrani, Valerio Pruneri, Morgan W. Mitchell

Published Dec 16, 2015• 116 citations
arXivHTMLPDF

Abstract

We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below 10^{-5} and strong metrological randomness assurances. This randomness generation strategy satisfies the stringent requirements for unpredictable basis choices in current "loophole-free Bell tests" of local realism [Hensen et al., Nature (London) 526, 682 (2015); Giustina et al., this issue, Phys. Rev. Lett. 115, 250401 (2015); Shalm et al., preceding Letter, Phys. Rev. Lett. 115, 250402 (2015)].

DOI
10.1103/physrevlett.115.250403

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Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.
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Experimental violations of Bell inequalities are in general vulnerable to so-called loopholes. In this work, we analyze the characteristics of a loophole-free Bell test with photons, closing simultaneously the locality, freedom-of-choice, fair-sampling (i.e., detection), coincidence-time, and memory loopholes. We pay special attention to the effect of excess predictability in the setting choices due to nonideal random-number generators. We discuss necessary adaptations of the Clauser-Horne and Eberhard inequality when using such imperfect devices and---using Hoeffding's inequality and Doob's optional stopping theorem---the statistical analysis in such Bell tests.
Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private randomness generated during a Bell test can be directly quantified from the observed correlations, without the need to process these data into an inequality. The frequency with which the different measurement settings are used during the Bell test can also be taken into account. This improved analysis turns out to be very relevant for Bell tests performed with a finite collection efficiency. In particular, applying our technique to the data of a recent experiment (Christensen et al 2013 Phys. Rev. Lett. 111 130406), we show that about twice as much randomness as previously reported can be potentially extracted from this setup.