Ontological Models, Preparation Contextuality and Nonlocality Manik Banik Email author Some Sankar Bhattacharya Sujit K. Choudhary Amit Mukherjee Arup Roy Article First Online: 08 October 2014 Received: 24 April 2014 Accepted: 19 September 2014 DOI :
10.1007/s10701-014-9839-4

Cite this article as: Banik, M., Bhattacharya, S.S., Choudhary, S.K. et al. Found Phys (2014) 44: 1230. doi:10.1007/s10701-014-9839-4
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Abstract 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.

Keywords Ontological model Preparation contextuality Nonlocality Bell’s theorem Recently, M. S. Leifer have written a review on \(\psi \) -ontology theorems [32 ]. Among many open questions listed in there one is concerned about preparation contextuality proof for any mixed quantum state. This question is addressed in our paper and we have answered affirmatively.

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Authors and Affiliations Manik Banik Email author Some Sankar Bhattacharya Sujit K. Choudhary Amit Mukherjee Arup Roy 1. Physics and Applied Mathematics Unit Indian Statistical Institute Kolkata India 2. Institute of Physics Bhubaneswar India