Many-qutrit Mermin inequalities with three measurement settings

TL;DR

This paper derives Mermin inequalities for three-qutrit systems with three measurement settings, showing stronger violations of local realism and larger GHZ contradictions than previous two-setting approaches, with eigenvalues scaling as 3^N.

Contribution

It introduces new Mermin inequalities for qutrits with three measurement settings, enhancing the strength of quantum violations and the number of GHZ contradictions.

Findings

Quantum eigenvalues scale as 3^N, faster than 2^N with two settings.

Stronger violations of local realism than previous two-setting inequalities.

Number of GHZ contradictions increases exponentially with system size.

Abstract

Mermin inequalities are derived for systems of three-state particles (qutrits) employing three local measurement settings. These establish perfect correlations which violate local realistic bounds more strongly than those previously reported with two bases. The quantum eigenvalue of the Mermin operator grows as the dimension of the Hilbert space, $3^N$, rather than $2^N$, as obtained with two measurement bases. The number of distinct GHZ contradictions also increases as $3^N$.