Mermin inequalities for perfect correlations

TL;DR

This paper derives optimal Bell inequalities for perfect correlations in all classes of graph states with fewer than seven qubits, revealing new inequalities and states with high decoherence resistance.

Contribution

It introduces new Bell inequalities for graph states, including twelve previously unknown, and identifies states with maximal violation and enhanced decoherence resistance.

Findings

Twelve new Bell inequalities discovered.

Four states match GHZ violation levels but are more decoherence-resistant.

Optimal inequalities for all graph states with n<7 qubits provided.

Abstract

Any n-qubit state with n independent perfect correlations is equivalent to a graph state. We present the optimal Bell inequalities for perfect correlations and maximal violation for all classes of graph states with n < 7 qubits. Twelve of them were previously unknown and four give the same violation as the Greenberger-Horne-Zeilinger state, although the corresponding states are more resistant to decoherence.