Measurement Theory Based on the Truth Values Violates Local Realism

Abstract

We investigate the violation factor of the Bell-Mermin inequality. Until now, we use an assumption that the results of measurement are +/- 1. In this case, the maximum violation factor is 2((n- 1)/ 2). The quantum predictions by n-partite Greenberger-Horne-Zeilinger (GHZ) state violate the Bell-Mermin inequality by an amount that grows exponentially with n. Recently, a new measurement theory based on the truth values is proposed (Nagata and Nakamura, Int. J. Theor. Phys. 55: 3616, 2016). The values of measurement outcome are either + 1 or 0. Here we use the new measurement theory. We consider multipartite GHZ state. It turns out that the Bell-Mermin inequality is violated by the amount of 2((n- 1)/ 2). The measurement theory based on the truth values provides the maximum violation of the Bell- Mermin inequality.