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

TL;DR

This paper investigates how superselection rules, especially particle number SSR, affect the ability to violate Bell inequalities, showing that suitable reference frames can enable such violations despite SSR constraints.

Contribution

It demonstrates that reference frames prepared with local operations can enable Bell inequality violations under superselection rules, highlighting the importance of reference frame properties.

Findings

Separable reference frames can facilitate Bell violations under SSR.

Superselection-induced variance characterizes the non-local properties of reference frames.

Bell tests should be adapted for experimental scenarios involving superselection rules.

Abstract

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.