^{1}

^{*}

^{2}

^{*}

We investigate the violation factor of the original Bell-Mermin inequality. Until now, we have used an assumption that the results of measurement are
. In this case, the maximum violation factor is as follows:
and
. 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
. 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:
and
. Thus the original Bell-Mermin inequality is satisfied by the new measurement theory. We propose the following conjecture:
*All the two-orthogonal-settings experimental correlation functions admit local realistic theories irrespective of a state if we use the new measurement theory.*

As a famous physical theory, the quantum theory (cf. [

On the other hand, from the incompleteness argument of Einstein, Podolsky, and Rosen (EPR) [

The other is the no-hidden-variables theorem of Kochen and Specker (KS theorem) [

Mermin considers the Bell-EPR theorem in a multipartite state. He derives multipartite Bell inequality [

As for the KS theorem, it is begun to research the validity of the KS theorem by using inequalities (see Refs. [

Leggett-type nonlocal hidden-variable theory [

Recently, it is discussed that von Neumann’s theory does not meet the Deutsch-Jozsa algorithm [

Further, an additional condition for Bell experiments for accepting local realistic theories is discussed [

Therefore we consider the significance of the value

An important note here is that we use the original Bell-Mermin inequality. We want to investigate whether all Bell inequalities [

In this paper, we investigate the violation factor of the Bell-Mermin inequality. Until now, we have used an assumption that the results of measurement are ±1. Recently, the new measurement theory is proposed [

Let us consider n particles

Let us consider the following GHZ state:

We have the following experimental result

where the local results of measurements are

On the other hand, let us consider the original Bell-Mermin inequality. We consider C as

where

The maximum of C is equal to the real part of a product of complex numbers each of which has magnitude of

Therefore, we have a violation of the Bell-Mermin inequality with the following factor

that is

We have

Hence, the Bell-Mermin inequality is satisfied irrespective of the number of particles. And the experimental correlation functions (measurement outcome is

In conclusion, we have investigated the violation factor of the Bell-Mermin inequality. Until now, we have used an assumption that the results of measurement are ±1. Recently, a new measurement theory has been proposed. The values of measurement outcome have been

KojiNagata,TadaoNakamura, (2015) Analysis of Bell-Type Experiments and Its Local Realism. Journal of Applied Mathematics and Physics,03,898-902. doi: 10.4236/jamp.2015.37109