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Bell violation using entangled photons without the fair-sampling assumption


The violation of a Bell inequality is an experimental observation that forces the abandonment of a local realistic viewpoint—namely, one in which physical properties are (probabilistically) defined before and independently of measurement, and in which no physical influence can propagate faster than the speed of light1,2. All such experimental violations require additional assumptions depending on their specific construction, making them vulnerable to so-called loopholes. Here we use entangled photons to violate a Bell inequality while closing the fair-sampling loophole, that is, without assuming that the sample of measured photons accurately represents the entire ensemble3. To do this, we use the Eberhard form of Bell’s inequality, which is not vulnerable to the fair-sampling assumption and which allows a lower collection efficiency than other forms4. Technical improvements of the photon source5,6 and high-efficiency transition-edge sensors7 were crucial for achieving a sufficiently high collection efficiency. Our experiment makes the photon the first physical system for which each of the main loopholes has been closed, albeit in different experiments.

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Figure 1: Principle of the experiment.
Figure 2: Measurement set-up.
Figure 3: Eberhard J value computed from up to five measurements of recorded data.

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We acknowledge M. Schmidt of Physikalisch-Technische Bundesanstalt in Berlin, Germany, for assistance with setting up the TES-SQUID system. This work was supported by the ERC (Advanced Grant number QIT4QAD 227844), the Austrian Science Fund (FWF) under projects SFB F4008 and CoQuS, the grant Q-ESSENCE (number 248095), QAP (number 15848), the Marie Curie Research Training Network EMALI (number MRTN-CT-2006-035369) and the John Templeton Foundation. This work was also supported by the NIST Quantum Information Science Initiative (QISI), an agency of the US Government.

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Authors and Affiliations



M.G. designed and carried out the experiment, and analysed data. A.M. designed and carried out the experiment. S.R. provided theoretical analysis, designed and carried out the experiment, and analysed data. B.W. designed and carried out the experiment. J.K. provided theoretical analysis, and analysed data. J.B., A.L., B.C., T.G. and S.W.N. provided experimental and conceptual assistance. R.U. designed the experiment and provided experimental, organizational and conceptual assistance. A.Z. conceived the research and guided the experiment. All authors wrote the manuscript.

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Correspondence to Marissa Giustina or Anton Zeilinger.

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The authors declare no competing financial interests.

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Giustina, M., Mech, A., Ramelow, S. et al. Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227–230 (2013).

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