Quantum Reference Frames in Arbitrary Charge Sectors: Accessibility of Global Properties from Internal Perspectives

Abstract: A fundamental question in the field of quantum reference frames concerns what global properties of a system can be determined by observers operating entirely from within that system. We investigate this question by extending both the perspectival and perspective-neutral approaches beyond the commonly studied zero total momentum case to arbitrary fixed charge sectors. When the entire system, including the reference frames, moves at a fixed total momentum $P$ relative to an external frame, this global charge becomes encoded in the quantum states and transformations between reference frames. Our extension leads to modified relative states and observables with QRF transformations that induce an additional $P$-dependent phase, treating all charge sectors as equally fundamental. By granting the internal observers successively more access and resources, we identify under which conditions they can infer the total momentum. These results clarify the relationship between major QRF approaches -- perspectival, perspective-neutral, operational, and extra-particle -- showing how their differing conclusions stem from different assumptions about which observables are deemed accessible from within. Our findings cast light on the relation between local and global perspectives and raise fundamental questions about scenarios where no global perspective exists, contributing to a deeper understanding of relationality and the role of perspectives in quantum theory.