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Entanglement Theory Quantum Correlations Quantum Foundations

A hidden-variables version of Gisin's theorem

arXiv

Authors: Kazuo Fujikawa, Koichiro Umetsu

Year

2014

Paper ID

47110

Status

Preprint

Abstract Read

~2 min

Abstract Words

160

Citations

N/A

Abstract

It is generally assumed that {\em local realism} represented by a noncontextual and local hidden-variables model in d=4 such as the one used by Bell always gives rise to CHSH inequality |langle Brangle|leq 2. On the other hand, the contraposition of Gisin's theorem states that the inequality |langle Brangle|leq 2 for arbitrary parameters implies (pure) separable quantum states. The fact that local realism can describe only pure separable quantum states is naturally established in hidden-variables models, and it is quantified by G\({bf a},{bf b}\)= 4\[langle ψ|P\({bf a}\)otimes P\({bf b}\)|ψrangle-langle ψ|P\({bf a}\)otimes{bf 1}|ψranglelangle ψ|{bf 1}otimes P\({bf b}\)|ψrangle\]=0 for any two projection operators P\({bf a}\) and P\({bf b}\). The test of local realism by the deviation of G\({bf a},{bf b}\) from G\({bf a},{bf b}\)=0 is shown to be very efficient using the past experimental setup of Aspect and his collaborators in 1981.

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It is generally assumed that em local realism represented by a noncontextual and local hidden-variables model in d=4 such as the one used by Bell always gives rise to CHSH...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1410.1702 [2] arXiv https://arxiv.org/abs/1410.1702 [3] Publisher https://arxiv.org/abs/1410.1702

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