Bell inequalities with continuous angular variables

TL;DR

This paper develops Bell inequalities tailored for bipartite quantum systems with continuous angular variables, enabling the detection of non-locality through correlated measurements, and proposes experimental approaches for such tests.

Contribution

It introduces Bell inequalities for continuous angular variables, extending non-locality tests beyond discrete systems and linking them to CHSH inequalities in a novel way.

Findings

Derived Bell inequalities for angular variables.

Showed equivalence to superpositions of CHSH inequalities.

Suggested feasible experiments for non-locality testing.

Abstract

We consider bipartite quantum systems characterized by a continuous angular variable \theta \in [-\pi, \pi[, 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.