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Abstract: The Bell and Leggett-Garg tests offer operational ways to demonstrate thatnon-classical behavior manifests itself in quantum systems, andexperimentalists have implemented these protocols to show that classicalworldviews such as local realism and macrorealism are false, respectively.Previous theoretical research has exposed important connections between moregeneral Bell inequalities and polyhedral combinatorics. We show here thatgeneral Leggett-Garg inequalities are closely related to the cut polytope ofthe complete graph, a geometric object well-studied in combinatorics. Buildingon that connection, we offer a family of Leggett-Garg inequalities that are nottrivial combinations of the most basic Leggett-Garg inequalities. We then showthat violations of macrorealism can occur in surprising ways, by giving anexample of a quantum system that violates the new -pentagon- Leggett-Garginequality but does not violate any of the basic -triangle- Leggett-Garginequalities.



Author: David Avis, Patrick Hayden, Mark M. Wilde

Source: https://arxiv.org/







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