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The Significance of Measurement Independence for Bell Inequalities and Locality

  • Michael J. W. HallEmail author
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 183)

Abstract

A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems performing the measurement, via some common cause. Hence, to derive no-go results such as Bell inequalities, an assumption of measurement independence is crucial. It is a surprisingly strong assumption—less than 1 / 15 bits of prior correlation suffice for a local model of the singlet state of two qubits—with ramifications for the security of quantum communication protocols. Indeed, without this assumption, any statistical correlations whatsoever—even those which appear to allow explicit superluminal signalling—have a corresponding local deterministic model. It is argued that ‘quantum nonlocality’ is bad terminology, and that measurement independence does not equate to ‘experimental free will’. Brans’ 1988 model is extended to show that no more than \(2\log d\) bits of prior correlation are required for a local deterministic model of the correlations between any two d-dimensional quantum systems.

Keywords

Measurement Dependence Singlet State Quantum Correlation Bell Inequality Statistical Completeness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I thank Cyril Branciard, Antonio Di Lorenzo, Jason Gallicchio, Nicolas Gisin, Valerio Scarani, Joan Vaccaro, Mark Wilde and Howard Wiseman for various stimulating discussions on this topic over the past few years. This work was supported by the ARC Centre of Excellence CE110001027.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith UniversityBrisbaneAustralia

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