Bell violation using entangled photons without the fair-sampling assumption
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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 light. 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 ensemble. 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 forms. Technical improvements of the photon source and high-efficiency transition-edge sensors 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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As the CHSH inequality is minimally violated in an optically realised system, the randomness output is also very small (with min-entropy of Hmin=7.2×10^-5 in each run), and the randomness generation rate is 0.4 bits per s.
“As the CHSH inequality is minimally violated in an optically realised system, 64,65 the randomness output is also very small (with min-entropy of H min =7.2 × 10 -5 in each run), and the randomness generation rate is 0.4 bits per s.”
From Quantum random number generation (2016) · cites this paper as [64]
The Experiment section reports an optical experiment with entangled photons and a Bell-inequality violation. But the paper explicitly says it tests Eberhard’s inequality, not CHSH, and our copy does not report a min-entropy of 7.2 × 10⁻⁵ per run or a randomness-generation rate of 0.4 bits per second (searched for those figures and randomness generation). (LLM, conf=0.87)
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- Authors
- Giustina, M., Mech, A., Ramelow, S., Wittmann, B., Kofler, J., Beyer, J., Lita, A., Calkins, B., Gerrits, T., Nam, S. W., Ursin, R., & Zeilinger, A.
- Affiliations
- Austrian Academy of Sciences (AT)
- University of Vienna (AT)
- Physikalisch-Technische Bundesanstalt (DE)
- National Institute of Standards and Technology (US)
- Corresponding author
- Giustina, Marissa
- Zeilinger, Anton
- ORCID
- Venue
- Nature
- Published
- 2013-04-14
- Volume
- 497
- Issue
- 7448
- Pages
- 227-230
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2009502003
- Cited by
- 660
- References
- 30
- Citations by year
- 2026: 15 · 2025: 21 · 2024: 20 · 2023: 52 · 2022: 31 · 2021: 44 · 2020: 42 · 2019: 59 · 2018: 26 · 2017: 35 · 2016: 109 · 2015: 79 · 2014: 73 · 2013: 35 · 2012: 15
- FWCI
- 50.80
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Nature Cell Biology
- Funders
- John Templeton Foundation
- Austrian Science Fund
- National Institute of Standards and Technology
- FP7 Ideas: European Research Council (227844)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Semiconductor Quantum Structures and Devices
- Keywords
- Bell inequality violation, entangled photons, local realism, transition edge sensors, photon pair sources, collection efficiency, quantum foundations
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