More non-locality in the three-qubit Greenberger-Horne-Zeilinger state

TL;DR

This paper investigates the non-local properties of noisy three-qubit GHZ states, demonstrating that additional measurement settings can lower the threshold for non-locality detection below 1/2, with the lowest threshold found at approximately 0.496.

Contribution

It introduces new Bell inequalities with more measurement settings that lower the non-locality threshold for three-qubit GHZ states below 1/2, including detailed methods and a large set of tight inequalities.

Findings

Non-locality threshold lowered to approximately 0.496 with 5x5x5 settings.

Additional measurement settings enable detection of non-locality at lower visibilities.

Over 10,000 tight Bell inequalities identified for v<1/2.

Abstract

The non-local properties of the noisy three-qubit Greenberger-Horne-Zeilinger (GHZ) states parameterized by the visibility 0<v<1 are investigated. Based on the violation of the 2x2x2-setting Mermin inequality, the noisy three-qubit GHZ states are non-local 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 5x5x5 settings, whereas the most economical one in number of settings corresponds to 3x3x4 settings. The method which enabled us to obtain these results, and in particular the about 10000 tight Bell inequalities giving v<1/2 are also discussed in detail.