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.

12 pages, two figures

References in corpus (7)

• Multi-photon entanglement in high dimensions
• Mermin inequalities for perfect correlations
• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
• Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
• Operational approach to Bell inequalities: applications to qutrits
• Quantum Contextuality with Stabilizer States
• Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox

Cited by in corpus (10)

• Twisted Photons: New Quantum Perspectives in High Dimensions
• Experimental GHZ Entanglement beyond Qubits
• Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits
• Scientific intuition inspired by machine learning generated hypotheses
• Observation of Genuine High-dimensional Multi-partite Non-locality in Entangled Photon States
• The power of qutrits for non-adaptive measurement-based quantum computing
• Maximally entangled real states and SLOCC invariants: the 3-qutrit case
• Unconditionally separating noisy ${\mathsf{QNC}}^0$ from bounded polynomial threshold circuits of constant depth
• Graph-theoretic insights on the constructability of complex entangled states
• Qudit Clauser-Horne-Shimony-Holt Inequality and Nonlocality from Wigner Negativity