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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Harrigan, N., Spekkens, R.W.: Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys. 40, 125–157 (2010)
Leifer, M.S.: Is the quantum state real? An extended review of \(\psi \)-ontology theorems. Quanta 3, 67 (2014)
Pusey, M.F., Barrett, J., Rudolph, T.: On the reality of the quantum state. Nat. Phys. 8, 476 (2012)
Hall, M.J.W.: Generalisations of the recent Pusey–Barrett–Rudolph theorem for statistical models of quantum phenomena. arXiv:1111.6304
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)
Hardy, L.: Are quantum states real? Int. J. Mod. Phys. B 27, 1345012 (2013)
Aaronson, S., Bouland, A., Chua, L., Lowther, G.: \(\psi \)-Epistemic theories: the role of symmetry. Phys. Rev. A 88, 032111 (2013)
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)
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)
Ballentine, L.: Ontological models in quantum mechanics: what do they tell us? (2014). arXiv:1402.5689
Maroney, O.J.E.: How statistical are quantum states? (2012). arXiv:1207.6906
Maroney, O.J.E.: A brief note on epistemic interpretations and the Kochen–Speker theorem. (2012). arXiv:1207.7192
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bandyopadhyay, S., Banik, M., Bhattacharya, S.S. et al. Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory. Found Phys 47, 265–273 (2017). https://doi.org/10.1007/s10701-016-0058-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-016-0058-z