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Foundations of Physics

, Volume 47, Issue 2, pp 265–273 | Cite as

Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory

  • Somshubhro Bandyopadhyay
  • Manik Banik
  • Some Sankar Bhattacharya
  • Sibasish Ghosh
  • Guruprasad Kar
  • Amit Mukherjee
  • Arup Roy
Article
  • 196 Downloads

Abstract

We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism comparable to that in quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.

Keywords

Onotological model Outcome-indeterminism Preparation-measurement reciprocity 

Notes

Acknowledgements

MB, GK, SG, and SB would like to thank Ravi Kunjwal for many helpful discussions. MB, GK, and SB would like to acknowledge The Institute of Mathematical Sciences, Chennai for supporting a visit during which part of this work was completed. AM acknowledges support from the CSIR Project 09/03 (0148)/2012-EMR-I. SB is supported in part by DST-SERB Project SR/S2/LOP-18/2012.

References

  1. 1.
    Harrigan, N., Spekkens, R.W.: Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys. 40, 125–157 (2010)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Leifer, M.S.: Is the quantum state real? An extended review of \(\psi \)-ontology theorems. Quanta 3, 67 (2014)CrossRefGoogle Scholar
  3. 3.
    Pusey, M.F., Barrett, J., Rudolph, T.: On the reality of the quantum state. Nat. Phys. 8, 476 (2012)CrossRefGoogle Scholar
  4. 4.
    Hall, M.J.W.: Generalisations of the recent Pusey–Barrett–Rudolph theorem for statistical models of quantum phenomena. arXiv:1111.6304
  5. 5.
    Colbeck, R., Renner, R.: Is a systems wave function in one-to-one correspondence with its elements of reality? Phys. Rev. Lett. 108, 150402 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    Hardy, L.: Are quantum states real? Int. J. Mod. Phys. B 27, 1345012 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Aaronson, S., Bouland, A., Chua, L., Lowther, G.: \(\psi \)-Epistemic theories: the role of symmetry. Phys. Rev. A 88, 032111 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    Patra, M.K., Pironio, S., Massar, S.: No-go theorem for \(\psi \)-epistemic models based on a continuity assumption. Phys. Rev. Lett. 111, 090402 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    Lewis, P.G., Jennings, D., Barrett, J., Rudolph, T.: Distinct quantum states can be compatible with a single state of reality. Phys. Rev. Lett. 109, 150404 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Ballentine, L.: Ontological models in quantum mechanics: what do they tell us? (2014). arXiv:1402.5689
  11. 11.
    Maroney, O.J.E.: How statistical are quantum states? (2012). arXiv:1207.6906
  12. 12.
    Maroney, O.J.E.: A brief note on epistemic interpretations and the Kochen–Speker theorem. (2012). arXiv:1207.7192

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Somshubhro Bandyopadhyay
    • 1
  • Manik Banik
    • 2
  • Some Sankar Bhattacharya
    • 3
  • Sibasish Ghosh
    • 2
  • Guruprasad Kar
    • 3
  • Amit Mukherjee
    • 3
  • Arup Roy
    • 3
  1. 1.Department of Physics and Center for Astroparticle Physics and Space ScienceBose InstituteKolkataIndia
  2. 2.Optics & Quantum Information GroupThe Institute of Mathematical SciencesChennaiIndia
  3. 3.Physics and Applied Mathematics UnitIndian Statistical InstituteKolkataIndia

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