Quantum generalizations of Bell's inequality
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For the spin-1/2 singlet, S_Bell can acquire the maximal value 2√2 allowed by quantum mechanics, known as the Cirel'son bound.
“For example the predictions for the spin-1/2 singlet give correlations for which S Bell can acquire the maximal value 2 √ 2 allowed by quantum mechanics, known as the Cirel'son 37 bound (Cirel'son, 1980;Landau, 1987).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Cirel'son, 1980
Cited by
Sorted by citations
Quantum information with continuous variables
Braunstein, S. L., & van Loock, P. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.513 · Cited by 3,858 · see citing works
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
Quantum nonlocality as an axiom
Popescu, S., & Rohrlich, D. (1994) · Foundations of Physics · doi:10.1007/bf02058098 · Cited by 1,562 · see citing works
Multiphoton entanglement and interferometry
Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., & Żukowski, M. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.777 · Cited by 1,410 · see citing works
Violating Bell inequality by mixed states: necessary and sufficient condition
Horodecki, R., Horodecki, P., & Horodecki, M. (1995) · Physics Letters A · doi:10.1016/0375-9601(95)00214-n · Cited by 884 · see citing works
Information processing in generalized probabilistic theories
Barrett, J. (2007) · Physical Review A · doi:10.1103/physreva.75.032304 · Cited by 768 · see citing works
Maximal violation of Bell's inequality for arbitrarily large spin
Gisin, N., & Peres, A. (1992) · Physics Letters A · doi:10.1016/0375-9601(92)90949-m · Cited by 398 · see citing works
Quantum analogues of the Bell inequalities. The case of two spatially separated domains
Tsirel'son, B. S. (1987) · Journal of Soviet Mathematics · doi:10.1007/bf01663472 · Cited by 381 · see citing works
Bell inequality, Bell states and maximally entangled states for n qubits
Gisin, N., & Bechmann-Pasquinucci, H. (1998) · Physics Letters A · doi:10.1016/s0375-9601(98)00516-7 · Cited by 270 · see citing works
Warm-starting quantum optimization
Egger, D. J., Mareček, J., & Woerner, S. (2021) · Quantum · doi:10.22331/q-2021-06-17-479 · Cited by 269 · see citing works
Beyond Bell's theorem: correlation scenarios
Fritz, T. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/10/103001 · Cited by 243 · see citing works
Lessons from the Information Paradox
Raju, S. (2020) · arXiv · doi:10.48550/arxiv.2012.05770 · Cited by 234
Quantum Theory: Informational Foundations and Foils
(2016) · Fundamental Theories of Physics · doi:10.1007/978-94-017-7303-4 · Cited by 178 · see citing works
Recent advances on integrated quantum communications
Orieux, A., & Diamanti, E. (2016) · Journal of Optics · doi:10.1088/2040-8978/18/8/083002 · Cited by 160 · see citing works
Mannalath, V., Mishra, S., & Pathak, A. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04175-y · Cited by 125 · see citing works
“Further, the PR box is known to be more non-local than quantum mechanics as the maximum value of Clauser-Horne-Shimony-Holt (CHSH) sum of correlations for QM is 2 √ 2 (Tsirelson bound) [223] while for that for PR box is 4.”
BackgroundRandomness requirement on the Clauser-Horne-Shimony-Holt Bell test in the multiple-run scenario
Yuan, X., Cao, Z., & Ma, X. (2015) · Physical Review A · doi:10.1103/physreva.91.032111 · Cited by 25 · see citing works
- Authors
- Cirel'son, B. S.
- Corresponding author
- Cirel'son, B. S.
- Venue
- Letters in Mathematical Physics
- Published
- 1980-03
- Volume
- 4
- Issue
- 2
- Pages
- 93-100
- ISSN
- 0377-9017 (ISSN-L)
- 1573-0530
- OpenAlex
- W2006638080
- Cited by
- 1,788
- References
- 0
- Citations by year
- 2026: 74 · 2025: 93 · 2024: 91 · 2023: 138 · 2022: 55 · 2021: 75 · 2020: 109 · 2019: 144 · 2018: 78 · 2017: 72 · 2016: 95 · 2015: 76 · 2014: 99 · 2013: 85 · 2012: 78
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Letters in Mathematical Physics (publishedVersion)
- 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 › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Bell inequalities, quantum correlations, quantum inequalities, quantum instruments, quantum nonlocality
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
