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TMF, 2007, Volume 152, Number 3, Pages 488–501 (Mi tmf6105)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized Bell inequality and a method for its verification

V. A. Andreev

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

Abstract: We use the reduced density matrix of the two-particle spin state to construct a generalized Bell–Clauser–Horne–Shimony–Holt inequality. For each specific state and under a special choice of the vectors $\vec a$, $\vec b$, $\vec c$, and $\vec d$, this inequality becomes an exact equality. We show how such vectors can be found using the reduced density matrix. Both sides of this equality have a specific numerical value. We indicate the connection of this number with the measure of entanglement of the two-particle spin state.

Keywords: quantum mechanics, entangled state, density matrix, Bell inequality

DOI: https://doi.org/10.4213/tmf6105

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English version:
Theoretical and Mathematical Physics, 2007, 152:3, 1286–1298

Bibliographic databases:

Received: 18.12.2006

Citation: V. A. Andreev, “Generalized Bell inequality and a method for its verification”, TMF, 152:3 (2007), 488–501; Theoret. and Math. Phys., 152:3 (2007), 1286–1298

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6105
  • http://mi.mathnet.ru/eng/tmf/v152/i3/p488

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Andreev, “The correlation Bell inequalities”, Theoret. and Math. Phys., 158:2 (2009), 196–209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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
    3. Quantum Electron., 50:5 (2020), 469–474  mathnet  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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