# Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory

@article{Bandyopadhyay2015ReciprocalOM,
title={Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory},
author={Somshubhro Bandyopadhyay and Manik Banik and Some Sankar Bhattacharya and Sibasish Ghosh and Guruprasad Kar and Amit Mukherjee and Arup Roy},
journal={Foundations of Physics},
year={2015},
volume={47},
pages={265-273}
}
• Published 10 August 2015
• Philosophy
• Foundations of Physics
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.
3 Citations
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## References

SHOWING 1-10 OF 40 REFERENCES
Ontological models predictively inequivalent to quantum theory.
• Philosophy, Physics
Physical review letters
• 2013
A model is described which violates the statement that no extension of quantum theory can have improved predictive power under a strong assumption of free choice of the experimental settings and validity of quantum mechanics for almost all states of a bipartite two-level system.
Ontological Models in Quantum Mechanics: What do they tell us?
The consequences of the theorems about ontological models are studied. "Maximally $\psi$-epistemic" is shown to be equivalent to the conjunction of two other conditions, each of which can be realized
No-go theorems for ψ-epistemic models based on a continuity assumption.
• Philosophy
Physical review letters
• 2013
This argument is different from the recent proof of Pusey, Barrett, and Rudolph and it already yields a nontrivial constraint on ψ-epistemic models using a single copy of the system in question.
Contextuality for preparations, transformations, and unsharp measurements
The Bell-Kochen-Specker theorem establishes the impossibility of a noncontextual hidden variable model of quantum theory, or equivalently, that quantum theory is contextual. In this paper, an
Einstein, Incompleteness, and the Epistemic View of Quantum States
• Philosophy
• 2007
It is shown that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem.
ψ-epistemic theories: The role of symmetry
• Philosophy
• 2013
Formalizing an old desire of Einstein, “ψ-epistemic theories” try to reproduce the predictions of quantum mechanics, while viewing quantum states as ordinary probability distributions over underlying
A brief note on epistemic interpretations and the Kochen-Specker theorem
One of the recent no-go theorems on \Psi-epistemic interpretations of quantum proves that there are no 'maximally epistemic' interpretations of quantum theory. The proof utilises similar arrangements
The statistical interpretation of quantum mechanics
The Statistical Interpretation of quantum theory is formulated for the purpose of providing a sound interpretation using a minimum of assumptions. Several arguments are advanced in favor of
Distinct quantum states can be compatible with a single state of reality.
• Physics
Physical review letters
• 2012
This work considers models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state-i.e., probability distributions for distinct quantum states overlap.
Is the Quantum State Real? An Extended Review of -ontology Theorems
The background needed for the novice in this area to understand the current status of the Pusey–Barrett–Rudolph Theorem is provided, and often overlooked subtleties should be of interest to the experts are discussed.