Interpreting quantum reference frame transformations through a simple example

TL;DR

This paper compares three different frameworks for quantum reference frame transformations using a simple three-qubit example, revealing their distinct rules and operational interpretations.

Contribution

It provides a clear analysis of three contemporary approaches to quantum reference frames through a simple example, highlighting their differences and operational meanings.

Findings

Each approach yields a different transformation rule.

States indistinguishable in one frame can be distinguishable in another.

The approaches reflect different attitudes towards global states and accessible information.

Abstract

Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference frames, with concomitantly different transformation rules. Here, we investigate a simple example of three qubit systems with $\mathbb{Z}_2$ symmetry in order to analyze physical and conceptual distinctions between three contemporary approaches to quantum reference frames -- dubbed perspective-neutral, extra particle and operational. By constructing two three-qubit states that are indistinguishable by observables relative to one frame but are distinguishable by observables relative to another, we show that each of the three approaches provides a distinct transformation rule, which may be understood to reflect differing attitudes towards the global state and the information that can be accessed by each frame. This helps us to shed light on the operational meaning of each approach and the contexts in which they may be most naturally applied.