A complete set of multidimensional Bell inequalities

A complete set of multidimensional Bell inequalities

We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf in [31], and by Ẑukowski and Brukner in [32], for the two-dimensional case. Our construction applies for the n parties, two-observables case, where each observable is d-valued. The d n inequalities obtained involve homogeneous polynomials. They define the facets of a polytope ...

Multidimensional Bell Inequalities and Quantum Cryptography

Tests of Bell inequalities

According to recent reports, the last loopholes in testing Bell’s inequality are closed. It is argued that the really important task in this field has not been tackled yet and that the leading experiments claiming to close locality and detection efficiency loopholes, although making very significant progress, have conceptual drawbacks. The important task is constructing quantum devices which wi...

Lifting Bell inequalities

A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings, or measurement outcomes. In this article, such “liftings” of Bell inequalities are studied. It is shown that if the original inequality defines a facet of the polytope of local joint outcome probabilities then the lifted one also defines a fac...

Error correcting bell inequalities.

Quantum error-correcting codes can protect multipartite quantum states from errors on some limited number of their subsystems (usually qubits). We construct a family of Bell inequalities which inherit this property from the underlying code and exhibit the violation of local realism, without any quantum information processing (except for the creation of an entangled state). This family shows no ...