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Bell inequalities with continuous angular variables

We consider bipartite quantum systems characterized by a continuous angular variable θ\in [-π, π[, representing, for instance, the position of a particle on a circle. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on bidimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, and we derive inequalities based on orientation correlation measurements. The introduced Bell-type inequalities open the perspective of new and simpler experiments to test non locality on a variety of quantum systems described by continuous variables.