Necessary and sufficient detection efficiency for the Mermin inequalities

TL;DR

This paper establishes the exact detection efficiency threshold for loophole-free Bell tests using Mermin inequalities and GHZ states, showing when local hidden variable models can or cannot replicate quantum correlations.

Contribution

It provides a precise necessary and sufficient detection efficiency threshold for Mermin inequality-based Bell tests, resolving a key question in quantum nonlocality experiments.

Findings

Threshold detection efficiency is n/(2n-2) for n-qubit GHZ states.

Below this threshold, local hidden variable models can simulate quantum predictions.

Above this threshold, quantum predictions cannot be simulated by local hidden variables.

Abstract

We prove that the threshold detection efficiency for a loophole-free Bell experiment using an $n$-qubit Greenberger-Horne-Zeilinger state and the correlations appearing in the $n$-partite Mermin inequality is $n/(2n-2)$. If the detection efficiency is equal to or lower than this value, there are local hidden variable models that can simulate all the quantum predictions. If the detection efficiency is above this value, there is no local hidden variable model that can simulate all the quantum predictions.