Leggett-Garg inequalities and the geometry of the cut polytope

Details Leggett-Garg inequalities and the geometry of the cut polytope Leggett-Garg inequalities and the geometry of the cut polytope

2010-04-21

arxiv.org/abs/1004.3818v1

Physical Review A 82, 030102(R) (2010)

Physics

Quantum Physics

5 pages, 1 figure

Scientific paper

10.1103/PhysRevA.82.030102

The Bell and Leggett-Garg tests offer operational ways to demonstrate that non-classical behavior manifests itself in quantum systems, and experimentalists have implemented these protocols to show that classical worldviews such as local realism and macrorealism are false, respectively. Previous theoretical research has exposed important connections between more general Bell inequalities and polyhedral combinatorics. We show here that general Leggett-Garg inequalities are closely related to the cut polytope of the complete graph, a geometric object well-studied in combinatorics. Building on that connection, we offer a family of Leggett-Garg inequalities that are not trivial combinations of the most basic Leggett-Garg inequalities. We then show that violations of macrorealism can occur in surprising ways, by giving an example of a quantum system that violates the new "pentagon" Leggett-Garg inequality but does not violate any of the basic "triangle" Leggett-Garg inequalities.

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