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arXiv:2510.13607 · Quantum

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

Published Jun 8, 2026• 1 citation
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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.

DOI
10.22331/q-2026-06-08-2126

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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.
A fundamental question in the field of quantum reference frames concerns what global properties of a system can be determined by observers operating entirely from within that system. We investigate this question by extending both the perspectival and perspective-neutral approaches beyond the commonly studied zero total momentum case to arbitrary fixed charge sectors. When the entire system, including the reference frames, moves at a fixed total momentum PPP relative to an external frame, this global charge becomes encoded in the quantum states and transformations between reference frames. Our extension leads to modified relative states and observables with QRF transformations that induce an additional PPP-dependent phase, treating all charge sectors as equally fundamental. By granting the internal observers successively more access and resources, we identify under which conditions they can infer the total momentum. These results clarify the relationship between major QRF approaches -- perspectival, perspective-neutral, operational, and extra-particle -- showing how their differing conclusions stem from different assumptions about which observables are deemed accessible from within. Our findings cast light on the relation between local and global perspectives and raise fundamental questions about scenarios where no global perspective exists, contributing to a deeper understanding of relationality and the role of perspectives in quantum theory.
A fundamental question in the field of quantum reference frames concerns what global properties of a system can be determined by observers operating entirely from within that system. We investigate this question by extending both the perspectival and perspective-neutral approaches beyond the commonly studied zero total momentum case to arbitrary fixed charge sectors. When the entire system, including the reference frames, moves at a fixed total momentum PPP relative to an external frame, this global charge becomes encoded in the quantum states and transformations between reference frames. Our extension leads to modified relative states and observables with QRF transformations that induce an additional PPP-dependent phase, treating all charge sectors as equally fundamental. By granting the internal observers successively more access and resources, we identify under which conditions they can infer the total momentum. These results clarify the relationship between major QRF approaches -- perspectival, perspective-neutral, operational, and extra-particle -- showing how their differing conclusions stem from different assumptions about which observables are deemed accessible from within. Our findings cast light on the relation between local and global perspectives and raise fundamental questions about scenarios where no global perspective exists, contributing to a deeper understanding of relationality and the role of perspectives in quantum theory.
We define the perspective of any quantum reference frame (QRF) and construct reversible transformations between different perspectives. Our construction is based on two principles motivated operationally by the change from relative to absolute coordinates and leads to an incoherent group averaging approach with general symmetry group. Thereby, it extends the framework of [arXiv:2110.13199] from ideal QRFs, which generally require infinite resources like energy or angular momentum, to non-ideal QRFs, with only finite resources. We find that the perspective of a non-ideal QRF deviates significantly from that of an ideal QRF: Firstly, systems described relative to a non-ideal QRF appear superselected. Secondly, the structure of the perspective of a non-ideal QRF attests that successive relational operations on a system lead to back-reaction on this QRF.
Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming the existence of external reference frame. To address these requirements, two approaches are proposed in the literature. The first one is an operational approach (F. Giacomini, et al, Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation between QRFs. The second approach attempts to derive the quantum transformation between QRFs from first principles (A. Vanrietvelde, et al, Quantum 4:225, 2020). Such first principle approach describes physical systems as symmetry induced constrained Hamiltonian systems. The Dirac quantization of such systems before removing redundancy is interpreted as perspective-neutral description. Then, a systematic redundancy reduction procedure is introduced to derive description from perspective of a QRF. The first principle approach recovers some of the results from the operational approach, but not yet include an important part of a quantum theory - the measurement theory. This paper is intended to bridge the gap. We show that the von Neumann quantum measurement theory can be embedded into the perspective-neutral framework. This allows us to successfully recover the results found in the operational approach, with the advantage that the transformation operator can be derived from the first principle. In addition, the formulation presented here reveals several interesting conceptual insights. For instance, the projection operation in measurement needs to be performed after redundancy reduction, and the projection operator must be transformed accordingly when switching QRFs. These results represent one step forward in understanding how quantum measurement should be formulated when the reference frame is also a quantum system.
In a quantum world, reference frames are ultimately quantum systems too – but what does it mean to "jump into the perspective of a quantum particle"? In this work, we show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operationally transparent framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and apply our results to a puzzle known as the `paradox of the third particle'. We argue that it can be reduced to the question of how to relationally embed fewer into more particles, and give a thorough physical and algebraic analysis of this question. This leads us to a generalization of the partial trace (`relational trace') which arguably resolves the paradox, and it uncovers important structures of constraint quantization within a simple quantum information setting, such as relational observables which are key in this resolution. While we restrict our attention to finite Abelian groups for transparency and mathematical rigor, the intuitive physical appeal of our results makes us expect that they remain valid in more general situations.
We generalize the notion of quantum reference frames (QRFs) to cases where the frame does not necessarily correspond to a tensor factor subsystem, but to a covariant quantum instrument. This unlocks a variety of physical applications: "frames of labeling" for indistinguishable particles, suggesting explanations for the symmetrization postulate and the absence of parastatistics, and yielding a transparent description of the entanglement of bosons and fermions; and relational clocks reproducing the Schrödinger equation exactly even when all subsystems are interacting or when there are frequency superselection sectors. Our work generalizes the perspective-neutral approach to QRFs pioneered by Höhn and co-authors, which we reconstruct from a simple operational scenario. We give a resource-theoretic grounding of this framework, and show how the notion of completely covariant operations explains the relevance of the charge-zero sector and the pure-state transformation behavior across perspectives. This also suggests operational clarifications of some aspects of constraint quantization, e.g. of the meaning of constraint equations such as C∣ψ⟩=0C|ψ\rangle=0C∣ψ⟩=0. Some of our results, such as our generalization of relationalization maps to instruments, apply more broadly to other QRF frameworks too, and they contribute to bridging the gap between operational quantum information theory and the internal QRF research program.