A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality

Details A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality

2003-06-19

arxiv.org/abs/quant-ph/0306129v2

Physics

Quantum Physics

6 pages, 1 figure, family of m-measurement n-outcome inequalities, and demonstration of non-locality sharing added

Scientific paper

10.1088/0305-4470/37/5/021

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. The new inequality also illustrates a sharing of bi-partite non-locality between three qubits: something not seen using the CHSH inequality. It also inspires us to discover a class of Bell inequalities with m possible n-outcome measurements on each particle.

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