Authors: Koji Nagata, Tadao Nakamura
We investigate the violation factor of the original Bell-Mermin inequality. Until now, we have used an assumption that the results of measurement are $\pm 1$. In this case, the maximum violation factor is as follows: $2^{(n-2)/2}(n={\rm even})$ and $2^{(n-1)/2}(n={\rm odd})$. The quantum predictions by $n$-partite Greenberger-Horne-Zeilinger state violate the Bell-Mermin inequality by an amount that grows exponentially with $n$. Recently, a new measurement theory is proposed [{K. Nagata and T. Nakamura, Int. J. Theor. Phys. {\bf 49}, 162 (2010)}]. The values of measurement outcome are $\pm 1/\sqrt{2}$. Here we use the new measurement theory. We consider a multipartite GHZ state. We use the original Bell-Mermin inequality. It turns out that the original Bell-Mermin inequality is satisfied irrespective of the number of particles. In this case, the maximum violation factor is as follows: $1/2(n={\rm even})$ and $1/\sqrt{2}(n={\rm odd})$. Thus the original Bell-Mermin inequality is satisfied by the new measurement theory. We propose the following conjecture: {\it All the two-orthogonal-settings experimental correlation functions admit local realistic theories irrespective of a state if we use the new measurement theory.}
Comments: Journal of Applied Mathematics and Physics, Volume 3, No.7 (2015), Page 898--902.
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