Avenues to generalising Bell inequalities. (23rd September 2022)

• Record Type: Journal Article
• Authors: Karczewski, Marcin; Scala, Giovanni; Mandarino, Antonio; Sainz, Ana Belén; Żukowski, Marek
• Is Part Of: Journal of physics. Volume 55:Number 38(2022)
• Publication Date: 2022-09-23
• Subjects: Bell inequalities -- Bell nonlocality -- non locally-realistic correlations -- foundations of quantum theory -- quantum information; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac8a28
• Languages: English
• ISSNs: 1751-8113

Abstract

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 references [2001 Phys. Rev. A 64 010102(R)] and [2001 Phys. Rev. A 64 032112]. 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 two 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.