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

TL;DR

This paper investigates quantum reference frames linked to non-compact groups like translations and boosts, highlighting the limitations of group averaging and analyzing the informational properties of reduced states for multi-particle Gaussian systems.

Contribution

It clarifies the effects of group averaging on non-compact groups and explores the informational aspects of reduced states in multi-particle quantum systems.

Findings

Group averaging leads to unphysical states for non-compact groups.

Reduced states on relative degrees of freedom are physically meaningful.

Analysis of Gaussian states reveals their informational properties in multi-particle systems.

Abstract

Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with non-compact groups, specifically the group of spatial translations and Galilean boosts. We begin by demonstrating how 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 non-compact groups. However, we show 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. [1]. We then study in detail the informational properties of this reduced state for systems of two and three particles in Gaussian states.