Randomness versus Nonlocality and Entanglement
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The outcomes obtained in Bell tests involving two-outcome measurements on two subsystems can, in principle, generate up to 2 bits of randomness. However, the maximal violation of the Clauser-Horne-Shimony-Holt inequality guarantees the generation of only 1.23 bits of randomness. We prove here that quantum correlations with arbitrarily little nonlocality and states with arbitrarily little entanglement can be used to certify that close to the maximum of 2 bits of randomness are produced. Our results show that nonlocality, entanglement, and randomness are inequivalent quantities. They also imply that device-independent quantum key distribution with an optimal key generation rate is possible by using almost-local correlations and that device-independent randomness generation with an optimal rate is possible with almost-local correlations and with almost-unentangled states.
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Although non-locality or entanglement certifies the randomness, the three quantities, non-locality, entanglement and randomness, are not equivalent.
“Although non-locality or entanglement certi fi es the randomness, the three quantities, non-locality, entanglement and randomness, are not equivalent. 68”
From Quantum random number generation (2016) · cites this paper as [68]
The Discussion (p. 9) says that non-locality is necessary for certifying randomness and that certified randomness is inequivalent to both non-locality and entanglement. The Abstract (p. 1) links randomness from measuring an entangled state to the additional condition that the outcomes violate a Bell inequality; it does not establish that entanglement alone certifies randomness. (LLM, conf=0.88)
Experimental — accuracy not yet measuredMaximum randomness generation does not require maximum non-local correlation or a maximum entangled state.
“Maximum randomness generation does not require maximum non-local correlation or a maximum entangled state.”
From Quantum random number generation (2016) · cites this paper as [68]
The Abstract (p. 1) says that correlations with arbitrarily small CHSH violations and states with arbitrarily little entanglement can certify randomness close to the two-bit maximum. The Discussion (p. 11) likewise says the authors establish arbitrarily close to two bits, not that the exact maximum is attained without maximal entanglement. The claim omits that qualification. (LLM, conf=0.86)
Experimental — accuracy not yet measuredIt is shown that 2 bits of randomness can be certified with little involvement of non-locality and entanglement.
“It is shown that 2 bits of randomness can be certi fi ed with little involvement of non-locality and entanglement. 68”
From Quantum random number generation (2016) · cites this paper as [68]
The Abstract (pp. 1–2) says correlations with arbitrarily little CHSH violation or states with arbitrarily little entanglement can certify randomness arbitrarily close to two bits. The claim captures the main finding but states two bits exactly and may imply that both resources are small in the same case; the cited passages establish neither qualification. (LLM, conf=0.88)
Experimental — accuracy not yet measured
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Self-citationFully device-independent model on quantum networks
Luo, M. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013203 · Cited by 29 · see citing works
Hardy's test as a device-independent dimension witness
Mukherjee, A., Roy, A., Bhattacharya, S. S., Das, S., Gazi, M. R., & Banik, M. (2015) · Physical Review A · doi:10.1103/physreva.92.022302 · Cited by 30 · see citing works
Device-Independent Quantum Key Distribution with Arbitrarily Small Nonlocality
Wooltorton, L., Brown, P. J., & Colbeck, R. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.210802 · Cited by 30 · see citing works
Experimental demonstration of robust self-testing for bipartite entangled states
Zhang, W.-H., Chen, G., Yin, P., Peng, X.-X., Hu, X., Hou, Z., Zhou, Z., Yu, S., Ye, X.-J., Zhou, Z., et al. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0120-0 · Cited by 27 · see citing works
Chen, S.-L., Ku, H.-Y., Zhou, W., Tura, J., & Chen, Y.-N. (2021) · Quantum · doi:10.22331/q-2021-09-28-552 · Cited by 26 · see citing works
Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game
Banik, M., Bhattacharya, S. S., Ganguly, N., Guha, T., Mukherjee, A., Rai, A., & Roy, A. (2019) · Quantum · doi:10.22331/q-2019-09-09-185 · Cited by 26 · see citing works
Semi-device-independent certification of indefinite causal order
Bavaresco, J., Araújo, M., Brukner, Č., & Quintino, M. T. (2019) · Quantum · doi:10.22331/q-2019-08-19-176 · Cited by 28 · see citing works
Gonzales-Ureta, J. R., Predojević, A., & Cabello, A. (2021) · Physical Review A · doi:10.1103/physreva.103.052436 · Cited by 26 · see citing works
Pan, A. (2021) · Physical Review A · doi:10.1103/physreva.104.022212 · Cited by 26 · see citing works
Coladangelo, A. (2018) · Physical Review A · doi:10.1103/physreva.98.052115 · Cited by 24 · see citing works
Generation of quantum randomness by probability estimation with classical side information
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Device-independent certification of one-shot distillable entanglement
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Device-independent certification of one-shot distillable entanglement
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Masini, M., Pironio, S., & Woodhead, E. (2022) · Quantum · doi:10.22331/q-2022-10-20-843 · Cited by 22 · see citing works
Self-citationDat, T. Q., & Duc, T. M. (2022) · Optik · doi:10.1016/j.ijleo.2022.168744 · Cited by 22 · see citing works
Coladangelo, A. (2020) · Quantum · doi:10.22331/q-2020-06-18-282 · Cited by 22 · see citing works
Cai, Z., Ren, C., Feng, T., Zhou, X., & Chen, J. (2024) · Physics Reports · doi:10.1016/j.physrep.2024.10.003 · Cited by 24 · see citing works
Revealing universal quantum contextuality through communication games
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Ab initio experimental violation of Bell inequalities
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Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game
Zhen, Y.-Z., Mao, Y., Zhang, Y., Xu, F., & Sanders, B. C. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.080801 · Cited by 21 · see citing works
Optimal Robust Self-Testing by Binary Nonlocal XOR Games
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Relationship between semi- and fully-device-independent protocols
Li, H.-W., Mironowicz, P., Pawłowski, M., Yin, Z., Wu, Y.-C., Wang, S., Chén, W., Hu, H., Guo, G., & Han, Z. (2013) · Physical Review A · doi:10.1103/physreva.87.020302 · Cited by 19 · see citing works
Semi-device-independent certification of indefinite causal order
Bavaresco, J., Araújo, M., Brukner, Č., & Quintino, M. T. (2019) · Kölner Universitäts PublikationsServer (Universität zu Köln) · Cited by 19 · see citing works
Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
Zjawin, B., Schmid, D., Hoban, M. J., & Sainz, A. B. (2023) · Quantum · doi:10.22331/q-2023-02-16-926 · Cited by 19 · see citing works
- Authors
- Acín, A., Massar, S., & Pironio, S.
- Affiliations
- Institució Catalana de Recerca i Estudis Avançats (ES)
- Université Libre de Bruxelles (BE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-03-09
- Volume
- 108
- Issue
- 10
- Pages
- 100402-100402
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1985083346
- Cited by
- 324
- References
- 23
- Citations by year
- 2026: 18 · 2025: 29 · 2024: 20 · 2023: 30 · 2022: 21 · 2021: 28 · 2020: 27 · 2019: 55 · 2018: 21 · 2017: 11 · 2016: 14 · 2015: 16 · 2014: 13 · 2013: 19 · 2012: 2
- FWCI
- 15.63
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Random lasers and scattering media
- Keywords
- randomness generation, nonlocality, entanglement, Bell tests, CHSH inequality, device-independent quantum key distribution, device-independent randomness generation, quantum correlations
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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