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

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.

References in corpus (9)

• Reference frames, superselection rules, and quantum information
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Quantification and scaling of multipartite entanglement in continuous variable systems
• Quantum communication using a bounded-size quantum reference frame
• How to observe a coherent superposition of an atom and a molecule
• Kinematics and dynamics in noninertial quantum frames of reference
• Communication between inertial observers with partially correlated reference frames
• Building all Time Evolutions with Rotationally Invariant Hamiltonians
• A relational approach to quantum reference frames for spins

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