Speaker
Description
The tensor product rule for composing subsystems is central to information-theoretic formulations of Quantum Theory. Adopting a relational view, we describe the adding and removing of subsystems in a quantum reference frame (QRF) for finite discrete translations following E. Castro-Ruiz, O. Oreshkov (2025). We show that textbook compositional rules only hold in a QRF perspective if the reference system is compatible with a `classical' external state. This issue is closely related to the so-called paradox of the third particle. An initial frame perspective can be inconsistent with the existence of an extra system in some relative state, making information of potentially far away systems appear to affect locally the description relative to a frame. There is, however, a way to recover the tensor product rule for any QRF by an invariance-preserving unitary map on the setup, as long as if it is redefined to include the external observer. We show how this procedure induces a modified adding rule for subsystems with a physical interpretation. We make an analogy between the map applied to a quantum frame, which recovers the standard adding properties, and changes of coordinates in classical physics which, via the equivalence principle, make non-inertial frames appear inertial. The procedure also recovers transformations from inequivalent QRF approaches without projections, hinting at a conceptual framework where different formalisms are consistent at the same time.