On the CHSH Form of Bell’s Inequalities

Samuel L. Braunstein, A. Mann, M. Revzen

We show that mixed states can produce maximal violations in the Bell inequality due to Clauser, Horne, Shimony, and Holt (CHSH). This follows from the degeneracy of the operator which is naturally associated with the Bell inequality (here called the Bell operator). We have calculated the form of all the eigenvalues for the generic CHSH Bell operator. Finally, we consider several examples which demonstrate the utility of studying the eigenvalues and eigenvectors of the Bell operator.

Binbin Liu, Jing Wang, Ming Li +2 more

Gábor Hofer‐Szabó

G. Coddens

We point out a loophole in the derivation of the Bell inequalities in the form proposed by Clauser, Horne, Shimony and Holt (CHSH). In this derivation it is assumed that statistical independence is a necessary consequence of locality, but this is not a logical necessity.

Jing‐Ling Chen, Dong-Ling Deng

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multipartite $d$-dimensional systems. All the Bell inequalities based on this generalization take the same simple form as the CHSH inequality. For small systems, numerical results show that the new inequalities are tight and we believe this is also valid for higher-dimensional systems. Moreover, the new inequalities are relevant to the previous ones and, for bipartite systems, our inequality is equivalent to the Collins-Gisin-Linden-Masser-Popescu inequality.

Enrico G. Beltrametti, Maciej Mączyński