Effect of the unpolarized spin state in spin-correlation measurement of two protons produced in the 12C(d,2He) reaction

In this note we discuss the effect of the unpolarized state in the spin-correlation measurement of the $^1S_0$ two-proton state produced in 12C(d,2He) reaction at the KVI, Groningen. We show that in the presence of the unpolarized state the maximal violation of the CHSH-Bell inequality is lower than the classical limit if the purity of the state is less than $ \sim \verb+70%+$. In particular, for the KVI experiment the violation of the CHSH-Bell inequality should be corrected by a factor $\sim\verb+10%+$ from the pure $^1S_0$ state.