Relative subsystems and quantum reference frame transformations

TL;DR

This paper develops a new framework for quantum reference frame transformations from first principles, allowing reversible transformations dependent only on the reference frames and systems, and introduces an extra particle to encode quantum features.

Contribution

It derives a general, principled approach to quantum reference frame transformations using standard quantum theory, expanding beyond previous models and including additional degrees of freedom.

Findings

Transformations depend only on reference frames and systems of interest.

Framework valid for a broad class of symmetry groups.

Introduction of an 'extra particle' encoding quantum features.

Abstract

Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous proposals could yield reversible transformations between arbitrary quantum reference frames only when applied to the whole universe. In contrast, here we derive quantum reference frame transformations from first principles, using only standard quantum theory. Our framework, naturally based on incoherent rather than coherent group averaging, yields reversible transformations that only depend on the reference frames and system of interest. We find more general transformations than those studied so far, which are valid only in a restricted subspace. Importantly, our framework contains additional degrees of freedom in the form of an "extra particle," which carries information about the quantum features of reference frame states. Our formalism is valid for a broad range of symmetry groups. We study the centrally extended Galilei group specifically, highlighting key differences from previous proposals.