Avenues to generalising Bell inequalities

Abstract

Characterizing the set of all Bell inequalities is a notably hard task. An insightful method of solving it in case of Bell correlation inequalities for scenarios with two dichotomic measurements per site - for arbitrary number of parties - was given in Refs. [Phys. Rev. A 64, 010102(R) (2001)] and [Phys. Rev. A 64, 032112 (2001)]. Using complex-valued correlation functions, we generalize their approach to a broader class of Bell scenarios, in which the parties may choose from more than 2 multi-outcome measurements. Although the resulting families of Bell inequalities are not always tight, their coefficients have an intuitively understandable structure.We probe their usefulness by numerically testing their ability to detect Bell nonclassicality in simple interferometric experiments. Moreover, we identify a similar structure in the CGLMP inequality expressed in a correlation-based form, which allows us to generalise it to three parties.

arXiv comment14 pages, 1 figure. Comments are welcome. V2: Minor edits, citations added. V3: minor edits

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• On the Fidelity Robustness of CHSH--Bell Inequality via Filtered Random States
• Insights into Quantum Contextuality and Bell Nonclassicality: A Study on Random Pure Two-Qubit Systems
• Bounding conditional entropy of bipartite states with Bell operators
• Optimal and robust error filtration for quantum information processing
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations