Quantum reference frames and deformed symmetries

TL;DR

This paper investigates how quantum reference frames and their measurement back-action could lead to deformed symmetries akin to doubly special relativity, revealing additional effects relevant to quantum gravity.

Contribution

It provides an analysis of symmetry deformation effects in a quantum system with relational observables, highlighting potential complexities in quantum gravity scenarios.

Findings

Supports the idea of symmetry deformation due to measurement back-action

Identifies additional effects that may obscure symmetry deformation

Uses a well-studied quantum information model for analysis

Abstract

In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system undergoes an unavoidable measurement "back-action" that modifies its properties. In a quantum-gravitational setting, it has been argued that such a back-action may produce effects that are described at an effective level as a form of deformed (or doubly) special relativity. We examine this possibility using a simple constrained system that has been extensively studied in the context of quantum information. While our conclusions support the idea of a symmetry deformation, they also reveal a host of other effects that may be relevant to the context of quantum gravity, and could potentially conceal the symmetry deformation.