Analysis of Bell-Type Experiments and Its Local Realism

We investigate the violation factor of the original Bell-Mermin inequality. Until now, we have used an assumption that the results of measurement are ±1. In this case, the maximum violation factor is as follows: ( ) ( ) −2 2 2 = even n n and ( ) ( ) −1 2 2 = odd n n . 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, International Journal of Theoretical Physics, 49, 162 (2010)]. The values of measurement outcome are ±1 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 = even n and ( ) 1 2 = odd n . Thus the original Bell-Mermin inequality is satisfied by the new measurement theory. We propose the following conjecture: All the twoorthogonal-settings experimental correlation functions admit local realistic theories irrespective of a state if we use the new measurement theory.