Hannover 2013 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 13: Quantum information: Concepts and methods I
Q 13.2: Talk
Monday, March 18, 2013, 14:15–14:30, E 214
Bell inequalities from variable elimination methods — •Costantino Budroni1 and Adan Cabello2 — 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, D-57068 Siegen,Germany — 2Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
Complete sets of tight Bell inequalities are necessary and sufficient conditions for the existence of local hidden variable models describing a given measurement scenario. They are facets of Pitowsky’s correlation polytope and are usually obtained from its extreme points by solving the hull problem. While there are algorithms that find all the facets of a given correlation polytope, the time required to compute them grows exponentially as the number of settings increases. This method has therefore been applied only to simple cases with a reduced number of settings.
In this talk an alternative method based on a combination of algebraic results on extensions of measures and variable elimination methods, e.g., the Fourier-Motzkin method, will be presented. Non-trivial cases where our method overcomes some of the computational difficulties associated with the hull problem will be discussed.