Proposed Experiment to Test Local Hidden-Variable Theories
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A theorem of Bell, proving that certain predictions of quantum mechanics are inconsistent with the entire family of local hidden-variable theories, is generalized so as to apply to realizable experiments. A proposed extension of the experiment of Kocher and Commins, on the polarization correlation of a pair of optical photons, will provide a decisive test between quantum mechanics and local hidden-variable theories.
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For any hidden-variable theories and arbitrary angles, the Bell parameter satisfies |S| ≤ 2, equivalent to a visibility of coincidence probability V ≤ 0.71 in both H-V and D-A bases.
“It can be proved that for any HVTs and arbitrary angles, Bell parameter satisfies inequality |S|≤2 which is equivalent to the visibility of coincidence probability V≤0.71 in both H-V and D-A basis [54], [76], [77].”
From Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source (2021) · cites this paper as [76]
The paper’s generalization of Bell’s theorem derives a bound for local hidden-variable theories, with locality and setting-independent hidden-variable distributions stated as assumptions (indexed Abstract section; page unavailable). Its discussion of inequality (2b) applies the bound to polarizer orientations, but the cited passages do not state a Bell parameter S or an equivalent coincidence-visibility limit of 0.71 in the H-V and D-A bases. The claim also overextends the result from local hidden-variable theories to any hidden-variable theory. (LLM, conf=0.90)
Experimental — accuracy not yet measuredOn the basis of the CHSH inequality, Fehr et al. and Pironio et al. proposed self-testing randomness expansion protocols against classical adversaries.
“On the basis of the Clauser -Horne -Shimony -Holt (CHSH) inequality, 56 Fehr et al. 57 and Pironio et al. 58 proposed self-testing randomness expansion protocols against classical adversaries.”
From Quantum random number generation (2016) · cites this paper as [56]
Any joint probability distribution satisfying assumptions O, L, and F must satisfy Bell inequalities, specifically the Clauser-Horne-Shimony-Holt inequality S ≤ 2.
“Any joint probability distribution satisfying these assumptions must then satisfy Bell inequalities (9).”
From Experimental test of local observer independence (2019) · cites this paper as [10]
If one chooses a non-factorizable function S(s1,s2)=1/2(1+s1+s2-s1s2), the CHSH inequality is recovered.
“If one chooses a non-factorizable function S(s 1 , s 2 ), say, 1 2 (1 + s 1 + s 2 -s 1 s 2 ), the famous CHSH (Clauser, Horne, Shimony, and Holt, 1969) inequality is recovered”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Clauser, Horne, Shimony, and Holt, 1969
Spacetime curvature can affect quantum interference by reducing fringe visibility in a Mach-Zehnder interferometer.
“As an application of the general formalism, we demonstrate how spacetime curvature can affect quantum interference by reducing fringe visibility in a Mach-Zehnder interferometer, and how it reduces entanglement by testing the violation of the CHSH inequality [15] for a specific detector model.”
From Exactly solvable 2D model for photon propagation in curved space: loss of interference and Bell inequality violation (2022) · cites this paper as [15]
Spacetime curvature reduces entanglement by testing the violation of the CHSH inequality for a specific detector model.
“As an application of the general formalism, we demonstrate how spacetime curvature can affect quantum interference by reducing fringe visibility in a Mach-Zehnder interferometer, and how it reduces entanglement by testing the violation of the CHSH inequality [15] for a specific detector model.”
From Exactly solvable 2D model for photon propagation in curved space: loss of interference and Bell inequality violation (2022) · cites this paper as [15]
The CHSH inequality |AB + A'B' + A'B - AB'| ≤ 2 is fulfilled for classical random variables provided that measuring observables A, A' is not influenced in any way by measuring B, B' and vice versa.
“| AB + A B + AB -A B | 2, (53 ) with four dichotomic random observables A, A , B, B that each can only take values ±1.It is fulfilled for classical random variables provided that measuring observables A, A is not influenced in any way by measuring B, B and vice versa.”
From Exactly solvable 2D model for photon propagation in curved space: loss of interference and Bell inequality violation (2022) · cites this paper as [15]
The complete set of LF facets for N=3, O=2 consists of 932 facets.
“we obtain the complete set of 932 LF facets for this scenario.”
From A strong no-go theorem on the Wigner’s friend paradox (2020) · cites this paper as [38]
The paper’s proposed-experiment section discusses a local hidden-variable inequality and photon-polarizer measurements, not an enumeration of LF facets. Searches for “932 LF facets N=3 O=2” and for local-friendliness facets found no passage addressing the claimed count; page numbers were not available in our copy. (LLM, conf=0.78)
Experimental — accuracy not yet measuredThe computer simulation generates the correlation from polarization and coherence, giving a CHSH correlation of respectively 2 and 1 for a total of 3.
“The computer simulation generates the correlation from polarization and coherence, giving a CHSH correlation [1] of respectively 2 and 1 for a total of 3.”
From EPR Correlations Using Quaternion Spin (2024) · cites this paper as [1]
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Zwerger, M., Lanyon, B. P., Northup, T. E., Muschik, C. A., Dür, W., & Sangouard, N. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa7983 · Cited by 23 · see citing works
Complementarity and Information in “Delayed-choice for Entanglement Swapping”
Brukner, Č., Aspelmeyer, M., & Zeilinger, A. (2005) · Foundations of Physics · doi:10.1007/s10701-005-7355-2 · Cited by 22 · see citing works
EPR Correlations Using Quaternion Spin
Sanctuary, B. (2024) · Quantum Reports · doi:10.3390/quantum6030026 · Cited by 18 · see citing works
Experimental hierarchy of two-qubit quantum correlations without state tomography
Abo, S., Soubusta, J., Jiráková, K., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-35015-9 · Cited by 17 · see citing works
“The Bell nonlocality of a given two-qubit state ρ can be tested by the violation of the Bell inequality in the Clauser-Horne-Shimony-Holt (CHSH) form [61] |〈B〉ρ| ≡ ∣∣〈a·σ⊗(b+b′)·σ+a′·σ⊗(b−b′)·σ〉 ρ ∣∣ ≤ 2, (20)”
Motazedifard, A., Madani, S. A., Dashkasan, J. J., & Vayaghan, N. S. (2021) · Heliyon · doi:10.1016/j.heliyon.2021.e07384 · Cited by 16 · see citing works
Nonlocality in Bell’s Theorem, in Bohm’s Theory, and in Many Interacting Worlds Theorising
Ghadimi, M., Hall, M. J. W., & Wiseman, H. M. (2018) · Entropy · doi:10.3390/e20080567 · Cited by 13 · see citing works
Quaternion-Spin and Some Consequences
Sanctuary, B. (2023) · doi:10.20944/preprints202312.1277.v1 · Cited by 9 · see citing works
Evidence of quantum-entangled higher states of consciousness
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Spin Helicity and the Disproof of Bell’s Theorem
Sanctuary, B. (2024) · Quantum Reports · doi:10.3390/quantum6030028 · Cited by 5 · see citing works
Escolà-Gascón, Á., & Benito-León, J. (2025) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2025.04.025 · Cited by 4 · see citing works
Sun, Y., Sun, C.-W., Zhou, W., Yang, R., Duan, J.-C., Gong, Y.-X., Xu, P., & Zhu, S.-N. (2023) · Chinese Physics B · doi:10.1088/1674-1056/acd8b3 · Cited by 3 · see citing works
Marzlin, K.-P., & Kinach, M. P. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac4fbb · Cited by 1 · see citing works
- Authors
- Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A.
- Affiliations
- Columbia University (US)
- Boston University (US)
- Harvard University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1969-10-13
- Volume
- 23
- Issue
- 15
- Pages
- 880-884
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2028815089
- Cited by
- 7,573
- References
- 10
- Citations by year
- 2026: 314 · 2025: 423 · 2024: 423 · 2023: 429 · 2022: 336 · 2021: 376 · 2020: 345 · 2019: 385 · 2018: 321 · 2017: 317 · 2016: 378 · 2015: 343 · 2014: 322 · 2013: 298 · 2012: 308
- FWCI
- 4.33
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- Funders
- Goddard Space Flight Center
- 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 › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- local hidden variable theories, Bell's theorem, polarization correlation, quantum mechanics
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