A theoretical study bridges two previously separate ideas: transformations between quantum reference frames (QRF) and the "trajectory-sharpening" effect that arises when a system is correlated with an effective negative-mass frame. The authors show that this sharpening admits a natural interpretation as a shift to the frame of a negative-mass system, thus linking an operational phenomenon with a formal concept of quantum mechanics for composite systems.

In a minimal model of free particles with arbitrary signed masses, the researchers identify the Einstein-Podolsky-Rosen-type observables responsible for the effect with a pair of commuting relational observables. Under the instantaneous QRF transformation, these observables are mapped to operators local to distinct subsystems. In addition, the corresponding relational trajectory is reproduced by the dynamical QRF transformation, in which the transformed relational position acquires an explicit time dependence.

The paper also introduces QRF-invariant sharpness measures for relational trajectories and derives monogamy relations: a trajectory cannot be made simultaneously arbitrarily sharp with respect to two distinct negative-mass frames. However, sharpness can reside in a collective reference mode encoded across two physical systems, even when neither constituent alone provides an arbitrarily sharp reference. In other words, sharpness can be distributed rather than localized in a single constituent frame.

These results provide an operational and potentially experimentally relevant interpretation of QRF transformations for continuous-variable systems, a domain that until now lacked concrete experimental consequences.