Foundations of Physics

, Volume 44, Issue 11, pp 1230–1244 | Cite as

Ontological Models, Preparation Contextuality and Nonlocality

  • Manik Banik
  • Some Sankar Bhattacharya
  • Sujit K. Choudhary
  • Amit Mukherjee
  • Arup Roy


The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some \(\psi \)-epistemic models without any use of Bell’s inequality. In particular, nonlocality of a non maximally \(\psi \)-epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger’s steerability of the maximally entangled state of two qubits (Leifer and Maroney, Phys Rev Lett 110:120401, 2013). In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality.


Ontological model Preparation contextuality Nonlocality Bell’s theorem 



It is our great pleasure to acknowledge G. Kar for various discussions, suggestions and help in proving the results. M. B. acknowledges private communications with M. S. Leifer about stronger non-maximal \(\psi \)-epistemicity. Discussion with S. Ghosh is gratefully acknowledged. S. K. C. is thankful to the Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata where a major part of this work was done when he was visiting the unit. A. M. acknowledges support from the CSIR Project 09/093(0148)/2012-EMR-I. S. K. C. acknowledges support from CSIR, Govt. of India. We also like to thank an anonymous referee for useful suggestions.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Manik Banik
    • 1
  • Some Sankar Bhattacharya
    • 1
  • Sujit K. Choudhary
    • 2
  • Amit Mukherjee
    • 1
  • Arup Roy
    • 1
  1. 1.Physics and Applied Mathematics UnitIndian Statistical InstituteKolkataIndia
  2. 2.Institute of PhysicsBhubaneswarIndia

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