Beyond Bell's theorem: correlation scenarios

@article{Fritz2012BeyondBT,
  title={Beyond Bell's theorem: correlation scenarios},
  author={Tobias Fritz},
  journal={New Journal of Physics},
  year={2012},
  volume={14},
  pages={103001}
}
  • T. Fritz
  • Published 22 June 2012
  • Computer Science
  • New Journal of Physics
Bell's theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a correlation scenario, and Bell's theorem then discards those local hidden variable… 

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References

SHOWING 1-10 OF 61 REFERENCES
Bell’s theorem without inequalities
It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the
Bell's Inequalities and Density Matrices: Revealing "Hidden" Nonlocality.
  • Popescu
  • Physics
    Physical review letters
  • 1995
TLDR
For mixed states, correlations arising from a single ideal measurement on each system may obey standard Bell inequalities, yet when each system is subjected to a sequence of ideal measurements the correlations are nonlocal.
Information processing in generalized probabilistic theories
TLDR
A framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others, is introduced, and a tensor product rule for combining separate systems can be derived.
On the Einstein-Podolsky-Rosen paradox
THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional
How much measurement independence is needed to demonstrate nonlocality?
TLDR
A connection is demonstrated between models that weaken the assumption that measurement settings are freely chosen by the observers, allowing partial correlation, and models that allow classical communication between the distant parties, including models that exploit the detection loophole.
Local deterministic model of singlet state correlations based on relaxing measurement independence.
  • M. Hall
  • Physics
    Physical review letters
  • 2010
TLDR
A simple measure of the degree of measurement independent is defined for correlation models, and it is shown that all spin correlations of a singlet state can be modeled via giving up just 14% of measurement independence.
A classification of hidden-variable properties
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked
Proposed Experiment to Test Local Hidden Variable Theories.
A theorem of Bell, proving that certain predictions of quantum mechanics are inconsistent with the entire family of local hidden-variable theories, is generalized so as to apply to realizable
On the free-will postulate in Quantum Mechanics
The so-called "free will axiom" is an essential ingredient in many discussions concerning hidden variables in quantum mechanics. In this paper we argue that "free will" can be defined in different
Random numbers certified by Bell’s theorem
TLDR
It is shown that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness, and it is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device.
...
...