Mermin inequalities for perfect correlations in many-qutrit systems

Abstract

The existence of GHZ contradictions in many-qutrit systems was a long-standing theoretical question until it's (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets identified in those proofs. These employ a weighted sum of observables, called M, in which every term has the chosen GHZ state as an eigenstate with eigenvalue unity. The quantum prediction for M is then just the number of concurrent observables, and this grows asymptotically as 2^N/3 as the number of qutrits (N) goes to infinity. The maximum classical value falls short for every N, so that the quantum to classical ratio (starting at 1.5 when N=3), diverges exponentially (~ 1.064^N) as N goes to infinity, where the system is in a Schroedinger cat-like superposition of three macroscopically distinct states.