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Non-Contextual and Local Hidden-Variable Model for the Peres–Mermin and Greenberger–Horne–Zeilinger Systems

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Abstract

A hidden-variable model for quantum–mechanical spin, as represented by the Pauli spin operators, is proposed for systems illustrating the well-known no-hidden-variables arguments by Peres (Phys Lett A 151:107–108, 1990) and Mermin (Phys Rev Lett  65:3373–3376, 1990) and by Greenberger et al. (Bell’s theorem, quantum theory, and conceptions of the universe, Kluwer, Dordrecht, 1989). Both arguments rely on an assumption of non-contextuality; the latter argument can also be phrased as a non-locality argument, using a locality assumption. The model suggested here is compatible with both assumptions. This is possible because the scalar values of spin observables are replaced by vectors that are components of orientations.

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Notes

  1. See [10], chap.6.

  2. See [15] p. 365, [16] Sect. 4.5, [17] Sect. 3.3.

  3. See e.g. [22], p. 29.

  4. See [10] p. 121, [5] p. 3373.

  5. [5] p. 3375 (numbering of equations adapted).

  6. arXiv:1907.13073v2 (2019) (an extended version of this paper).

  7. See footnote 6, 3.1-3.2 for details of this interpretation.

  8. See footnote 6, Appendix A4 for details.

  9. See footnote 6, Appendix A3 for a proof.

  10. See the discussion in footnote 6, Appendix A4.

  11. See footnote 6, Appendix B.

  12. See again footnote 6, Appendix B.

  13. See footnote 6, Appendix C.

  14. See footnote 6, Appendix D.

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  1. Weimar, Germany

    Carsten Held

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Held, C. Non-Contextual and Local Hidden-Variable Model for the Peres–Mermin and Greenberger–Horne–Zeilinger Systems. Found Phys 51, 33 (2021). https://doi.org/10.1007/s10701-021-00409-0

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