Robust coincidence Bell inequalities for the noisy n-qutrit Greenberger-Horne-Zeilinger state

The general form of the coincidence Bell inequalities for an arbitrary (n, 2, 3) scenario [i.e., an n-party, two-setting, and three-dimensional system (qutrit) scenario] is presented. To detect the nonlocal properties of the noisy n-qutrit Greenberger-Horne-Zeilinger states, in this work we investigate the most robust (4,2,3)-scenario and (5,2,3)-scenario coincidence Bell inequalities. By deriving the most robust (n - 1)-party coincidence inequalities, we have established two tight and inequivalent (n, 2, 3) coincidence Bell inequalities with a visibility of 0.5 for n = 4 and, similarly, two tight and inequivalent (n, 2, 3) coincidence Bell inequalities with a visibility of 0.488785 for n = 5. These inequalities are all tight. To our knowledge, up to now these inequalities have been the most robust Bell inequalities for the corresponding scenarios. Our results are useful for building the iteration formula of (n, 2, 3)-scenario coincidence Bell inequalities with the lowest critical visibility.