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TMF, 2008, Volume 157, Number 1, Pages 99–115 (Mi tmf6266)  

This article is cited in 18 scientific papers (total in 18 papers)

EPR–Bohm experiment and Bell's inequality: Quantum physics meets probability theory

A. Yu. Khrennikov

Växjö University

Abstract: Our main aim in this paper is to inform the physics community (and especially experts in quantum information) about investigations of the problem of the probabilistic compatibility of a family of random variables: the possibility of realizing such a family based on a single probability measure (of constructing a single Kolmogorov probability space). These investigations were started a hundred years ago by Boole. The complete solution of the problem was obtained by the Soviet mathematician Vorobiev in the 1960s. It turns out that probabilists and statisticians obtained inequalities for probabilities and correlations that include the famous Bell's inequality and its generalizations.

Keywords: Bell's inequality, nonlocality, “death of reality”, probabilistic incompatibility of random variables, Boole's necessary condition, Vorobiev theorem, contextual description of the EPR–Bohm experiment


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English version:
Theoretical and Mathematical Physics, 2008, 157:1, 1448–1460

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Received: 07.09.2007
Revised: 09.11.2007

Citation: A. Yu. Khrennikov, “EPR–Bohm experiment and Bell's inequality: Quantum physics meets probability theory”, TMF, 157:1 (2008), 99–115; Theoret. and Math. Phys., 157:1 (2008), 1448–1460

Citation in format AMSBIB
\by A.~Yu.~Khrennikov
\paper EPR--Bohm experiment and Bell's inequality: Quantum physics meets
probability theory
\jour TMF
\yr 2008
\vol 157
\issue 1
\pages 99--115
\jour Theoret. and Math. Phys.
\yr 2008
\vol 157
\issue 1
\pages 1448--1460

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    This publication is cited in the following articles:
    1. Hess K., Michielsen K., De Raedt H., “Possible experience: From Boole to Bell”, EPL, 87:6 (2009), 60007, 6 pp.  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    2. Khrennikov A., “Detection model based on representation of quantum particles by classical random fields: Born's rule and beyond”, Found. Phys., 39:9 (2009), 997–1022  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Khrennikov A., “On the Physical Basis of Theory of “Mental Waves””, Neuroquantology, 8:4, Suppl. 1 (2010), S71–S80  crossref  isi  scopus
    4. Khrennikov A., “Classical and Quantum Probability for Biologists -Introduction”, Quantum Bio-Informatics III: From Quantum Information To Bio-Informatics, Qp-Pq Quantum Probability and White Noise Analysis, 26, 2010, 179–192  crossref  mathscinet  adsnasa  isi
    5. N. L. Chuprikov, “O sovmestimosti korpuskulyarnykh i volnovykh svoistv chastitsy v dvukhschelevom eksperimente”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(23) (2011), 235–242  mathnet  crossref
    6. Chuprikov N.L., “From a 1D Completed Scattering and Double Slit Diffraction to the Quantum-Classical Problem for Isolated Systems”, Found Phys, 41:9 (2011), 1502–1520  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. Broda B., Szanecki M., “On Possible Violation of the Clauser-Horne-Shimony-Holt Bell Inequality in a Classical Context”, J Phys Soc Japan, 80:6 (2011), 063001  crossref  adsnasa  isi  elib  scopus  scopus
    8. Khrennikov A., “Violation of Bell's Inequality and Postulate on Simultaneous Measurement of Compatible Observables”, Journal of Computational and Theoretical Nanoscience, 8:6 (2011), 1006–1010  crossref  isi  scopus  scopus
    9. Hess K., De Raedt H., Michielsen K., “Hidden Assumptions in the Derivation of the Theorem of Bell”, Phys. Scr., T151 (2012), 014002  crossref  adsnasa  isi  scopus
    10. Dzhafarov E.N., Kujala J.V., “All-Possible-Couplings Approach to Measuring Probabilistic Context”, PLoS One, 8:5 (2013), e61712  crossref  adsnasa  isi  scopus  scopus
    11. Dzhafarov E.N., Kujala J.V., “Order-Distance and Other Metric-Like Functions on Jointly Distributed Random Variables”, Proc. Amer. Math. Soc., 141:9 (2013), 3291–3301  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Dzhafarov E.N., Kujala J.V., “Contextuality Is About Identity of Random Variables”, Phys. Scr., T163 (2014), 014009  crossref  mathscinet  adsnasa  isi  scopus  scopus
    13. Dzhafarov E.N., Kujala J.V., “No-Forcing and No-Matching Theorems For Classical Probability Applied To Quantum Mechanics”, Found. Phys., 44:3 (2014), 248–265  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Dzhafarov E.N., Kujala J.V., “A Qualified Kolmogorovian Account of Probabilistic Contextuality”, Quantum Interaction, Qi 2013, Lecture Notes in Computer Science, 8369, eds. Atmanspacher H., Haven E., Kitto K., Raine D., Springer-Verlag Berlin, 2014, 201–212  crossref  mathscinet  isi  scopus  scopus
    15. Loubenets E.R., “On the existence of a local quasi hidden variable (LqHV) model for each N -qudit state and the maximal quantum violation of Bell inequalities”, Int. J. Quantum Inf., 14:4, SI (2016), 1640010  crossref  mathscinet  zmath  isi  elib  scopus
    16. Khrennikov A., “Bell Could Become the Copernicus of Probability”, Open Syst. Inf. Dyn., 23:2 (2016), 1650008  crossref  mathscinet  zmath  isi  elib  scopus
    17. Dzhafarov E.N., Kujala J.V., “Probabilistic Foundations of Contextuality”, Fortschritte Phys.-Prog. Phys., 65:6-8, SI (2017), 1600040  crossref  mathscinet  zmath  isi  scopus  scopus
    18. Baladron C., Khrennikov A., “Bell Inequality Violation in the Framework of a Darwinian Approach to Quantum Mechanics”, Eur. Phys. J.-Spec. Top., 227:15-16 (2019), 2119–2132  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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