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International Journal of Theoretical Physics

, Volume 57, Issue 7, pp 1996–2006 | Cite as

Field Extension of Real Values of Physical Observables in Classical Theory can Help Attain Quantum Results

  • Hai Wang
  • Asutosh Kumar
  • Minhyung Cho
  • Junde Wu
Article
  • 58 Downloads

Abstract

Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what would happen if physical observables are allowed to assume complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using local hidden variable model. Furthermore, we try to build a new type of hidden-variable theory of a single qubit based on the result.

Keywords

Observables Bell inequality GHZ problem Hidden variable model 

Notes

Acknowledgements

This project is supported by Research Fund, Kumoh National Institute of Technology.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Hai Wang
    • 1
  • Asutosh Kumar
    • 2
    • 3
  • Minhyung Cho
    • 4
  • Junde Wu
    • 1
  1. 1.School of Mathematics SciencesZhejiang UniversityHangzhouPeople’s Republic of China
  2. 2.Harish-Chandra Research Institute, HBNIAllahabadIndia
  3. 3.P. G. Department of PhysicsGaya College, Magadh UniversityGayaIndia
  4. 4.Department of Applied MathematicsKumoh National Institute of TechnologyKyungbukKorea

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