Abstract
Both quantum communication without a shared reference frame and the construction of a relational quantum theory require the notion of a quantum reference frame. Aspects of quantum reference frames associated with noncompact groups, specifically, the translation group and the group of Galilean boosts are analyzed. It is demonstrated that the usually employed group average, used to dispense of the notion of an external reference frame, leads to unphysical states when applied to reference frames associated with noncompact groups. However, it is shown that this average does lead naturally to a reduced state on the relative degrees of freedom of a system, which was previously considered by Angelo et al. (J Phys A 44:145304, 2011). The informational properties of this reduced state for systems of two and three particles in Gaussian states are characterized in detail.
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