The Perspectives of Non-Ideal Quantum Reference Frames

TL;DR

This paper extends the concept of quantum reference frames to non-ideal cases with finite resources, revealing how their perspectives differ from ideal frames and how they influence system descriptions and back-reaction effects.

Contribution

It introduces a framework for non-ideal quantum reference frames, deriving their perspectives from physical principles and analyzing the consequences of finite resources.

Findings

Non-ideal QRFs cause superselection in system descriptions.

Successive operations induce back-reaction on the QRF.

The perspective deviates from ideal frames due to resource limitations.

Abstract

We define the perspective of any quantum reference frame (QRF) and construct reversible transformations between different perspectives. This extends the framework of [arXiv:2110.13199] to non-ideal QRFs with finite resources such as energy or angular momentum. We derive a QRF's perspective starting from two physically motivated principles, leading to an incoherent group averaging approach. The perspective of a non-ideal QRF deviates significantly from that of a more intuitive ideal frame with infinite resources: Firstly, systems described relative to the QRF appear superselected. Secondly, the structure of the QRF perspective attests that successive operations on a system relative to the QRF leads to back-reaction onto the QRF due to its non-ideality.