Abstract
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.
Highlights
As a famous physical theory, the quantum theory gives accurate and at times remarkably accurate numerical predictions
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
The quantum predictions by n-partite GHZ state violate the Bell-Mermin inequality by an amount that grows exponentially with n
Summary
As a famous physical theory, the quantum theory (cf. [1]-[5]) gives accurate and at times remarkably accurate numerical predictions. Mermin considers the Bell-EPR theorem in a multipartite state. The quantum predictions by n-partite GHZ state violate the Bell-Mermin inequality by an amount that grows exponentially with n. Several multipartite Bell inequalities are reported [17]-[25] They say that the quantum predictions violate local hidden-variable theories by an amount that grows exponentially with n. The quantum predictions by n-partite uncorrelated state violate the inequality by an amount that grows exponentially with n. Bell inequalities [23]-[25] with two-orthogonal-settings per side are satisfied by the new measurement theory even the GHZ state. 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
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