Designing Bell inequalities from a Tsirelson bound

Abstract

We present a simple analytic bound on the quantum value of general correlation type Bell inequalities, similar to Tsirelson's bound. It is based on the maximal singular value of the coefficient matrix associated with the inequality. We provide a criterion for tightness of the bound and show that the class of inequalities where our bound is tight covers many famous examples from the literature. We describe how this bound helps to construct Bell inequalities, in particular inequalities that witness the dimension of the measured observables.

4 pages, 4 figures, published version

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• Simple conditions constraining the set of quantum correlations
• Trade-offs in multi-party Bell inequality violations in qubit networks
• Measurable criteria of generalized non-locality under the correlation symmetry
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Optimisation of Bell inequalities with invariant Tsirelson bound
• Undetectable Werner states using linear Bell inequalities
• Random and free observables saturate the Tsirelson bound for CHSH inequality
• Local hidden variable values without optimization procedures
• Platonic Bell inequalities for all dimensions
• Designing generalized elegant Bell inequalities in higher dimensions from a Tsirelson bound