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Physical Review A - Atomic, Molecular, and Optical Physics


The existence of Greenberger-Horne-Zeilinger (GHZ) contradictions in many-qutrit systems was a long-standing theoretical question until its (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 2N/3 as the number of qutrits N→∞. The maximum classical value falls short for every N≥3, so that the quantum to classical ratio (starting at 1.5 when N=3) diverges exponentially (∼1.064N) as N→∞, where the system is in a Schrödinger-cat-like superposition of three macroscopically distinct states.