Two-setting Bell Inequalities for Graph States

Toth, Geza; Guehne, Otfried; Briegel, Hans J.

Two-setting Bell Inequalities for Graph States

Authors

Toth, Geza

Guehne, Otfried

Briegel, Hans J.

Description

We present Bell inequalities for graph states with high violation of local realism. In particular, we show that there is a two-setting Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of two. These inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. We first present a method which assigns a Bell inequality for each graph vertex. Then for some families of graph states composite Bell inequalities can be constructed with a violation of local realism increasing exponentially with the number of qubits. We also suggest a systematic way for obtaining Bell inequalities with a high violation of local realism for arbitrary graphs.
8 pages including 2 figures, revtex4; minor changes