A relevant two qubit Bell inequality inequivalent to the CHSH inequality

By D. Collins, Nicolas Gisin. 2003

367 citations recorded by the source corpus.

We computationally investigate the complete polytope of Bell inequalities for two 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 three 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ed45082a2185918df43c303a30dc459bb8f4ffa1

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

All noncontextuality inequalities for the n-cycle scenario (2012, methodology): “We have provided the complete characterization of the associated set of classical correlations for an arbitrary number n of settings, the only other example of this kind being the Bell bipartite scenario with two observables for Alice and n for Bob [31, 32].”
A strong no-go theorem on the Wigner’s friend paradox (2019, neutral): “[30] Collins, D.”
Entanglement detection (2008, background): “For the 4322 case there are three new inequalities [340].”