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TMF, 2009, Volume 158, Number 2, Pages 234–249 (Mi tmf6311)  

This article is cited in 5 scientific papers (total in 5 papers)

The correlation Bell inequalities

V. A. Andreev

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We consider the Bell and Bell–Clauser–Horne–Shimony–Holt inequalities for two-particle spin states. It is known that these inequalities are violated in experimental verification. We show that this can be explained because these inequalities are proved for correlation functions of random variables that are totally unrelated to one another, while the verification is done using correlation functions in which random variables refer to a pair of particles forming a two-particle state. In the case of entangled states, these random functions are dependent, and their correlation coefficient is nonzero. We give inequalities that explicitly involve this correlation coefficient. For factorable and separable states, these inequalities coincide with the standard Bell and Bell–Clauser–Horne–Shimony–Holt inequalities.

Keywords: quantum mechanics, Bell inequality, spin state, correlation coefficient, hidden parameter, nonlocality, probability

DOI: https://doi.org/10.4213/tmf6311

Full text: PDF file (443 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 158:2, 196–209

Bibliographic databases:

Received: 13.02.2008
Revised: 21.05.2008

Citation: V. A. Andreev, “The correlation Bell inequalities”, TMF, 158:2 (2009), 234–249; Theoret. and Math. Phys., 158:2 (2009), 196–209

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nikitin N.V., Toms K.S., “Relativistic Generalization of Bell's Inequalities in Wigner's Form”, Phys Atomic Nuclei, 72:12 (2009), 2027–2038  crossref  adsnasa  isi  elib  scopus  scopus
    2. 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
    3. Nikitin N.V. Sotnikov V.P. Toms K.S., “Time-Dependent Bell Inequalities in a Wigner Form”, Mosc. Univ. Phys. Bull., 69:6 (2014), 480–487  crossref  mathscinet  adsnasa  isi  scopus  scopus
    4. Nikitin N.V., Sotnikov V.P., Toms K.S., “Investigation of Properties of Time-Dependent Bell Inequalities in Wigner'S Form For Nonstationary and Open Quantum Systems”, Phys. Atom. Nuclei, 78:7 (2015), 805–830  crossref  adsnasa  isi  elib  scopus  scopus
    5. Adam P. Andreev V.A. Man'ko M.A. Man'ko I V., “Symbols of Multiqubit States Admitting a Physical Interpretation”, J. Russ. Laser Res., 39:4 (2018), 360–375  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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