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Quantum communication without a shared reference frame or the construction ofa relational quantum theory requires the notion of a quantum reference frame.We analyze aspects of quantum reference frames associated with non-compactgroups, specifically the group of spatial translations and Galilean boosts. Webegin by demonstrating how the usually employed group average, used to dispenseof the notion of an external reference frame, leads to unphysical states whenapplied to reference frames associated with non-compact groups. However, weshow that this average does lead naturally to a reduced state on the relativedegrees of freedom of a system, which was previously considered by Angelo etal. [1]. We then study in detail the informational properties of this reducedstate for systems of two and three particles in Gaussian states.

Quantum reference frames associated with non-compact groups: the case of translations and boosts, and the role of mass