What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks

Guilhem Doat; Augustin Vanrietvelde

doi:10.22331/q-2026-06-08-2126

What can we do in a symmetry-constrained perspective? The importance of the total charge’s status in quantum reference frame frameworks

Guilhem Doat and Augustin Vanrietvelde

LTCI, Inria, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France

Published:	2026-06-08, volume 10, page 2126
Editor:	Andrea Di Biagio
Eprint:	arXiv:2510.13607v3
Doi:	https://doi.org/10.22331/q-2026-06-08-2126
Citation:	Quantum 10, 2126 (2026).

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Abstract

The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the mathematical level, they mainly differ in the kind of symmetry (either weak or strong) employed to constrain the system. We show that this mathematical difference corresponds to a fundamental physical question: whether the global charge associated to the symmetry group is accessible to symmetry-constrained observers. In this context, we formulate a definition of a perspective in terms of operational capacities, or lack thereof. Turning to consequences of adopting either approach, we discuss how adopting the weak approach induces an ambiguity in the momenta included in each perspective and bars from defining reversible QRF transformations. We then review and analyze the existing arguments motivating each approach, and show how they bear upon the problem of charge accessibility. Finally, we introduce a simple operational scenario in which upholding two reasonable physical postulates leads to the conclusion that internal observers could measure the global charge by 1/ performing a relativized interference measurement and 2/ classically communicating.

Featured image: Toy scenario considered in the paper, in which which Alice and Bob attempt to retrieve the $Z_2$ symmetry charge Eve attributes to the system.

Popular summary

The notion of symmetry is ubiquitous to the one of quantum reference frame (QRF). In this work, we render explicit how two different notions of symmetry coexist in the QRF literature, and show the physical consequences each of them entails. We then present a simple scenario in which the symmetry criteria best suited to the situation is derived from the operational abilities of internal agents.

► BibTeX data

@article{Doat2026whatcanwedoin,
  doi = {10.22331/q-2026-06-08-2126},
  url = {https://doi.org/10.22331/q-2026-06-08-2126},
  title = {What can we do in a symmetry-constrained perspective? {T}he importance of the total charge's status in quantum reference frame frameworks},
  author = {Doat, Guilhem and Vanrietvelde, Augustin},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2126},
  month = jun,
  year = {2026}
}

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[2] Sébastien Christophe Garmier, Ladina Hausmann, and Esteban Castro-Ruiz, "The Perspectives of Non-Ideal Quantum Reference Frames", arXiv:2512.19343, (2025).

[3] Matthew J. Lake and Marek L. Miller, "How many degrees of freedom describe a quantum N-particle state?", arXiv:2607.16988, (2026).

[4] Alessandro Palumbo and Luca Apadula, "Frame-Dependent Traces and the Third-Particle Paradox", arXiv:2607.21703, (2026).

[5] Augustin Vanrietvelde, "Specifying the operational meaning of quantum reference frames", arXiv:2607.03417, (2026).

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