Reference frames for Bell inequality violation in the presence of superselection rules

Superselection rules (SSRs) constrain the allowed states and operations in quantum theory. They limit preparations and measurements hence impact upon our ability to observe non-locality, in particular the violation of Bell inequalities. We show that a reference frame compatible with a particle number SSR does not allow observers to violate a Bell inequality if and only if it is prepared using only local operations and classical communication. In particular, jointly prepared separable reference frames are sufficient for obtaining violations of a Bell inequality. We study the size and non-local properties of such reference frames using superselection-induced variance. These results suggest the need for experimental Bell tests in the presence of superselection.