A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality

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  • 19 June 2003
Abstract
We computationally investigate the complete polytope of Bell inequalities for 2 particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection of this problem to the computationally hard NP problem. Despite this, we find that there are very few relevant inequivalent inequalities for small numbers. For example, in the case with 3 possible 2-outcome measurements on each particle, there is just one new inequality. We describe mixed 2-qubit states which violate this inequality but not the CHSH. Inspired by this inequality, we present a new class of Bell inequalities with n possible 2-outcome measurements on each particle and a further class with n possible 3-outcome measurements.

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