What can we do in a symmetry-constrained perspective? The importance of the total charge’s status in quantum reference frame frameworks
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Updated version: The authors have uploaded version v4 of this work to the arXiv which may contain updates or corrections not contained in the published version v3. The authors left the following comment on the arXiv:25+6 pages. Comments are welcome!AbstractThe 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 summaryThe 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} }► References [1] P. A. Hoehn, I. Kotecha, and F. M. 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Could not fetch ADS cited-by data during last attempt 2026-06-08 10:47:39: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Updated version: The authors have uploaded version v4 of this work to the arXiv which may contain updates or corrections not contained in the published version v3. The authors left the following comment on the arXiv:25+6 pages. Comments are welcome!AbstractThe 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 summaryThe 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} }► References [1] P. A. Hoehn, I. Kotecha, and F. M. Mele, ``Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics,'' arXiv:2308.09131 [quant-ph]. arXiv:2308.09131 [2] Y. Aharonov and L. Susskind, ``Charge Superselection Rule,'' Physical Review 155 (1967) 1428–1431. https://doi.org/10.1103/PhysRev.155.1428 [3] Y. Aharonov and T. Kaufherr, ``Quantum frames of reference,'' Physical Review D 30 (1984) 368–385. https://doi.org/10.1103/PhysRevD.30.368 [4] G. C. Wick, A. S. Wightman, and E. P. Wigner, ``Superselection rule for charge,'' Physical Review D 1 (1970) 3267–3269. https://doi.org/10.1103/PhysRevD.1.3267 [5] A. R. H. Smith, ``Communicating without shared reference frames,'' Physical Review A 99 (2019) 052315, arXiv:1812.08053 [quant-ph]. https://doi.org/10.1103/PhysRevA.99.052315 arXiv:1812.08053 [6] R. W. Spekkens and G. Gour, ``The resource theory of quantum reference frames: manipulations and monotones,'' New Journal of Physics. 10 no. 3, (2008) 033023, arXiv:0711.0043 [quant-ph]. https://doi.org/10.1088/1367-2630/10/3/033023 arXiv:0711.0043 [7] G. Gour, I. Marvian, and R. W. Spekkens, ``Measuring the quality of a quantum reference frame: The relative entropy of frameness,'' Physical Review A 80 no. 1, (2009) 012307, arXiv:0901.0943 [quant-ph]. https://doi.org/10.1103/PhysRevA.80.012307 arXiv:0901.0943 [8] S. D. Bartlett, T. Rudolph, and R. W. Spekkens, ``Reference frames, superselection rules, and quantum information,'' Reviews of Modern Physics 79 (2007) 555–609, arXiv:quant-ph/0610030. https://doi.org/10.1103/RevModPhys.79.555 arXiv:quant-ph/0610030 [9] L. Loveridge, P. Busch, and T. Miyadera, ``Relativity of quantum states and observables,'' Europhysics Letters 117 no. 4, (2017) 40004, arXiv:1604.02836 [quant-ph]. https://doi.org/10.1209/0295-5075/117/40004 arXiv:1604.02836 [10] L. Loveridge, T. Miyadera, and P. Busch, ``Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics,'' Foundations of Physics 48 no. 2, (2018) 135–198, arXiv:1703.10434 [quant-ph]. https://doi.org/10.1007/s10701-018-0138-3 arXiv:1703.10434 [11] T. Carette, J. Głowacki, and L. Loveridge, ``Operational Quantum Reference Frame Transformations,'' Quantum 9 (2025) 1680, arXiv:2303.14002 [quant-ph]. https://doi.org/10.22331/q-2025-03-27-1680 arXiv:2303.14002 [12] J. Głowacki, L. Loveridge, and J. Waldron, ``Quantum Reference Frames on Finite Homogeneous Spaces,'' International Journal of Theoretical Physics 63 no. 5, (2024) 137, arXiv:2302.05354 [quant-ph]. https://doi.org/10.1007/s10773-024-05650-7 arXiv:2302.05354 [13] E. Castro-Ruiz and O. Oreshkov, ``Relative subsystems and quantum reference frame transformations,'' Communications Physics 8 no. 1, (2025) 187, arXiv:2110.13199 [quant-ph]. https://doi.org/10.1038/s42005-025-02036-x arXiv:2110.13199 [14] F. Giacomini, ``Spacetime Quantum Reference Frames and superpositions of proper times,'' Quantum 5 (2021) 508, arXiv:2101.11628 [quant-ph]. https://doi.org/10.22331/q-2021-07-22-508 arXiv:2101.11628 [15] A. Ballesteros, F. Giacomini, and G. Gubitosi, ``The group structure of dynamical transformations between quantum reference frames,'' Quantum 5 (2021) 470, arXiv:2012.15769 [quant-ph]. https://doi.org/10.22331/q-2021-06-08-470 arXiv:2012.15769 [16] F. Giacomini, E. Castro-Ruiz, and Č. Brukner, ``Quantum mechanics and the covariance of physical laws in quantum reference frames,'' Nature Communications 10 no. 1, (2019) 494, arXiv:1712.07207 [quant-ph]. https://doi.org/10.1038/s41467-018-08155-0 arXiv:1712.07207 [17] A. Vanrietvelde, P. A. Hoehn, F. Giacomini, and E. Castro-Ruiz, ``A change of perspective: switching quantum reference frames via a perspective-neutral framework,'' Quantum 4 (2020) 225, arXiv:1809.00556 [quant-ph]. https://doi.org/10.22331/q-2020-01-27-225 arXiv:1809.00556 [18] A.-C. de la Hamette and T. D. Galley, ``Quantum reference frames for general symmetry groups,'' Quantum 4 (2020) 367, arXiv:2004.14292 [quant-ph]. https://doi.org/10.22331/q-2020-11-30-367 arXiv:2004.14292 [19] A.-C. de la Hamette, T. 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