On Bell-type inequalities

Yu-Chun Wu, Marek Żukowski

A technique, which we call homogenization, is applied to transform Clauser and Horne- (CH)-type Bell inequalities that contain lower-order correlations into CH, Shimony, and Holt- (CHSH)-type Bell inequalities, which are defined for highest-order correlation functions. A homogenization leads to inequalities involving more settings, that is, a choice of one more observable is possible for each party. We show that this technique preserves the tightness of Bell inequalities: A homogenization of a tight CH-type Bell inequality is still a tight CHSH-type Bell inequality. As an example, we obtain $3\ifmmode\times\else\texttimes\fi{}3\ifmmode\times\else\texttimes\fi{}3$ CHSH-type Bell inequalities by the homogenization of $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CH-type Bell inequalities derived by Sliwa [Phys. Lett. A 317, 165 (2003)].

Enrico G. Beltrametti, Carlo Del Noce, Maciej Mączyński

Asher Peres

Li‐Yi Hsu

We investigate the Bell-type inequalities of graph states. In this paper, Bell-type inequalities can be derived based on two kinds of the associated subgraphs of the graph states. First, the star subgraphs lead to the maximal violation of the modified Seevinck-Svetlichny inequalities. Second, cycle subgraphs lead to maximal violation of Bell-type inequalities. As a result, once the associated graph of a graph state is given, the corresponding Bell operators can be immediatedly determined using stabilizing generators. In the above Bell-type inequalities, two measurement settings for each party are required.

Marek Kanter

The usual Bell-type inequalities involve correlations between observables. Inequalities of the Bell-type are presented which involve correlations between the probabilities associated with states and which can be used as a test for hidden variables in quantum mechanics independent of the Bell inequalities. The inequalities are universal in the sense that they are valid for all separable metric state spaces, as opposed to the usual Bell inequalities whose specific form is a function of the state space of the candidate classical model. The inequalities are harder to prove than the usual Bell-type inequalities because no essential restrictions on the state space are made.

John Maddox