# Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems

@article{Sica2013LogicalDF, title={Logical Difficulty from Combining Counterfactuals in the GHZ-Bell Theorems}, author={Louis Sica}, journal={Applied Mathematics-a Journal of Chinese Universities Series B}, year={2013}, volume={2013}, pages={90-94} }

In eliminating the fair sampling assumption, the
Greenberger, Horne, Zeilinger (GHZ) theorem is believed to confirm Bell’s
historic conclusion that local hidden variables are inconsistent with the
results of quantum mechanics. The GHZ theorem depends on predicting the results
of sets of measurements of which only one may be performed. In the present
paper, the noncommutative aspects of these unperformed measurements are
critically examined. Classical examples and the logic of the GHZ…

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## References

SHOWING 1-10 OF 19 REFERENCES

Logical inconsistency in combining counterfactual results from non-commutative operations: Deconstructing the GHZ-Bell theorems

- Physics
- 2012

The Greenberger, Horne, Zeilinger (GHZ) theorem is critically important to consideration of the possibility of hidden variables in quantum mechanics. Since it depends on predictions of single sets of…

All quantum observables in a hidden-variable model must commute simultaneously

- Physics
- 2004

Under a standard set of assumptions for a hidden-variable model for quantum events we show that all observables must commute simultaneously. This seems to be an ultimate statement about the…

Bell's inequality violation due to misidentification of spatially non-stationary random processes

- Physics
- 2003

Abstract Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and non-local information. They satisfy Bell's inequality and exhibit spatial…

Going Beyond Bell’s Theorem

- Physics
- 1989

Bell’s Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one could…

Counterfactuals in Quantum Mechanics

- PhilosophyCompendium of Quantum Physics
- 2009

The truth value of acounterfactual is decided by the analysis of similarities between the actual and possible counterfactual worlds and a simple conditional is applied.

Correlations for a new Bell’s inequality experiment

- Mathematics
- 2002

Proofs of Bell’s theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate…

The Einstein, Podolsky, and Rosen Paradox in Atomic, Nuclear, and Particle Physics

- Physics
- 1998

Early Formulations. Bell's Inequality and its Elementary Background. Local Realism Versus Quantum Nonlocality. The EPR Paradox in Particle Physics. Proposed Solutions of the Paradox. Index.