An additional condition for Bell experiments for accepting local realistic theories.

We assume that one source of two uncorrelated spin-carrying particles emits them in a state, which can be described as a spin-1/2 bipartite pure uncorrelated state. We consider a Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) experiment with two-orthogonal-settings. We propose an additional condition for the state to be reproducible by the property of local realistic theories. We use the proposed measurement theory in order to construct the additional condition (Nagata and Nakamura in Int J Theor Phys 49:162, ). The condition is that local measurement outcome is $$\pm 1/\sqrt{2}$$ . Otherwise, such an experiment does not allow for the existence of local realistic theories even in the situation that all Bell-CHSH inequalities hold. Also we derive new set of Bell inequalities when local measurement outcome is $$\pm 1/\sqrt{2}$$ . [ABSTRACT FROM AUTHOR]