Partial list of bipartite Bell inequalities with four binary settings
arXiv:0711.3362 · doi:10.1016/j.physleta.2008.01.052
Abstract
We give a partial list of 26 tight Bell inequalities for the case where Alice and Bob choose among four two-outcome measurements. All tight Bell inequalities with less settings are reviewed as well. For each inequality we compute numerically the maximal quantum violation, the resistance to noise and the minimal detection efficiency required for closing the detection loophole. Surprisingly, most of these inequalities are outperformed by the CHSH inequality.
6 pages. Other inequalities welcome. Accepted for publication in Phys. Lett. A
References in corpus (8)
- Non-local correlations as an information theoretic resource
- A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
- Quantum non-locality in two three-level systems
- Detection loophole in asymmetric Bell experiments
- Minimum detection efficiency for a loophole-free atom-photon Bell experiment
- Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities
- A Zoology of Bell inequalities resistant to detector inefficiency
- Bell inequalities stronger than the CHSH inequality for 3-level isotropic states
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