What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks.

The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the mathematical level, they mainly differ in the kind of symmetry (either weak or strong) employed to constrain the system. We show that this mathematical difference corresponds to a fundamental physical question: whether the global charge associated to the symmetry group is accessible to symmetry-constrained observers. In this context, we formulate a definition of a perspective in terms of operational capacities, or lack thereof. Turning to consequences of adopting either approach, we discuss how adopting the weak approach induces an ambiguity in the momenta included in each perspective and bars from defining reversible QRF transformations. We then review and analyze the existing arguments motivating each approach, and show how they bear upon the problem of charge accessibility. Finally, we introduce a simple operational scenario in which upholding two reasonable physical postulates leads to the conclusion that internal observers could measure the global charge by 1/ performing a relativized interference measurement and 2/ classically communicating.