Polarization correlations of the Psi-plus Bell state ($E(\alpha ,\beta )=-\cos 2(\alpha +\beta )$)

For $|{\Psi }^{+}⟩=(|01⟩+|10⟩)/\sqrt{2}$, the Pauli operator correlations are $⟨XX⟩=1$, $⟨ZZ⟩=-1$, and $⟨XZ⟩=⟨ZX⟩=0$. Substituting the measurement of linear photon polarization into $⟨M(\alpha )\otimes M(\beta )⟩$ gives $\sin 2\alpha \sin 2\beta -\cos 2\alpha \cos 2\beta =-\cos 2(\alpha +\beta )$. In particular, opposite physical angles give perfect anticorrelation. The sum of angles here depends on this choice of Bell state and basis conventions.