1210.6742 (Alexey E. Rastegin)

Tests for quantum contextuality in terms of $q$-entropies    [PDF]

Alexey E. Rastegin

The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many properties similarly to the standard ones. In general, various formulations of Bell's theorem are based on the noncontextuality hypothesis. Using this hypothesis and properties of the conditional $q$-entropies, we derive information-theoretic inequalities of the Bell type for all $q\geq1$. A recently proposed example of five observations for three-level system is explicitly analyzed within the context of $q$-entropic formulation. As is shown, quantum mechanics predicts the violation of an entire family of $q$-entropic inequalities of Bell's type.

View original: http://arxiv.org/abs/1210.6742