Molecular orientation entanglement and temporal Bell-type inequalities

TL;DR

This paper extends Bell-type inequalities to continuous-variable molecular systems, demonstrating non-locality tests based on molecular orientation, with practical experimental considerations and robustness analysis.

Contribution

It introduces Bell-type inequalities for molecular orientation measurements, bridging continuous observables with non-locality tests and providing experimental feasibility insights.

Findings

Non-locality tests applicable to molecular orientation.

Derived inequalities are robust to noise.

Experimental scenarios for testing are feasible.

Abstract

We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett. {\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations between measurements of continuous observables performed on trapped molecular systems. We show that for some observables with a continuous spectrum which is bounded, one is able to construct non-locality tests sharing common properties with those for two-level systems. The specific observable studied here is molecular spatial orientation, and it can be experimentally measured for single molecules, as required in our protocol. We also provide some useful general properties of the derived inequalities and study their robustness to noise. Finally, we detail possible experimental scenarii and analyze the role played by different experimental parameters.