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  • Open Access

Interpreting quantum-reference-frame transformations through a simple example

Esteban Castro-Ruiz1, Thomas D. Galley1,2,3,*, and Leon Loveridge4

  • *Contact author: thomas.galley@universite-paris-saclay.fr
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Phys. Rev. A 114, 032201 – Published 2 September, 2026

DOI: https://doi.org/10.1103/czr8-dv1l

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 Z2 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 physical meaning of each approach and the contexts in which they may be most naturally applied.

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Phys. Rev. A 114, 032201– Published 2 September, 2026
  • Received 14 July 2026
  • Accepted 20 July 2026
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