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

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In this note we discuss the effect of the unpolarized state in the spin-correlation measurement of the ¹S₀ 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 +70%+. In particular, for the KVI experiment the violation of the CHSH-Bell inequality should be corrected by a factor +10%+ from the pure ¹S₀ state.