Nonclassicality threshold for the three-qubit Greenberger-Horne-Zeilinger state

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Abstract

The nonclassical properties of the noisy three-qubit Greenberger-Horne- Zeilinger (GHZ) states, ρv=v+(1-v)1/8 parameterized by the visibility 0≤v≤1 are investigated. Based on the violation of the 2×2×2-setting Mermin inequality, ρv is nonclassical for the parameter range 1/2<v≤1. It has been posed whether additional settings would allow to lower the threshold visibility. Here we report on Bell inequalities giving a threshold value smaller than v=1/2. This rules out the possibility of a local hidden variable model in the limit of v=1/2. In particular, the lowest threshold visibility we found is v=0.496057, attainable with 5×5×5 settings, whereas the most economical one in number of settings corresponds to 3×3×4 settings. The method which enabled us to obtain these results, and in particular the about 10 000 tight Bell inequalities giving v<1/2, are also discussed in detail.

Original languageEnglish
Article number042122
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume84
Issue number4
DOIs
Publication statusPublished - Oct 28 2011

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ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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