Tight Bell inequalities are facets of Pitowskys correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here, we present an alternative method based on a combination of algebraic results on extensions of measures and variable-elimination methods, e.g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements. © 2012 IOP Publishing Ltd.
Bell inequalities from variable-elimination methods
Budroni C.;
2012-01-01
Abstract
Tight Bell inequalities are facets of Pitowskys correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here, we present an alternative method based on a combination of algebraic results on extensions of measures and variable-elimination methods, e.g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements. © 2012 IOP Publishing Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
