Mermin inequalities for GHZ contradictions in many-qutrit systems

In view of recent experimental interest [1] in multi-qutrit entanglement properties, we provide here new Mermin inequalities for use in experimental tests of many-qutrit GHZ contradictions, first predicted only recently (2013). Mermin inequalities refer here to Bell-like inequalities in which the quantum predictions are not probabilistic, thus elevating hidden variables to the status of EPR elements of reality. Earlier Bell inequalities for qutrits [2] predate the discovery of GHZ contradictions, are based on non-concurrent observable sets, and hence cannot establish GHZ contradictions. The current Mermin inequalities are derived from those concurrent observable sets which produce GHZ contradictions, with the following results: (i) There is an operator $M$ defined for every $N \geq 4$, built on two measurement bases, whose quantum eigenvalue grows as $2^N$, maximum classical value more slowly ($1.879^N$), with quantum to classical ratio being never less than 1.39, and (ii) For $N=3$, there is an $M_3$, built on three local measurement bases, whose quantum to classical ratio is 3/2. [1] M. Malik et. al., {\it Nature Photonics}, {\bf 10}, 248 (2016), [2] W. Son et. al., {\it Phys Rev. Letters}, {\bf 96}, 060406 (2006).