Leggett-Garg inequalities and the geometry of the cut polytope
- School of Computer Science, McGill University, Montreal, Quebec, H3A 2A7 (Canada)
The Bell and Leggett-Garg tests offer operational ways to demonstrate that nonclassical 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 'pentagon' Leggett-Garg inequality but does not violate any of the basic 'triangle' Leggett-Garg inequalities.
- OSTI ID:
- 21448603
- Journal Information:
- Physical Review. A, Vol. 82, Issue 3; Other Information: DOI: 10.1103/PhysRevA.82.030102; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Investigation of properties of time-dependent bell inequalities in Wigner’s form for nonstationary and open quantum systems
Kochen-Specker theorem as a precondition for secure quantum key distribution