When reference frames are treated quantum mechanically, the subsystem structure of quantum systems is no longer absolute, but depends on the choice of the quantum reference frame (QRF). This raises a basic question: which dynamical properties are preserved across QRFs, and which depend on the physical reference used to define the system? We study this question in the general setting of open quantum systems. At the operational level, after a QRF transformation, the old reference frame and environmental degrees of freedom may be inaccessible and must therefore be traced out. This motivates the definition of reduced quantum-reference-frame channels: maps that connect the joint description in one frame to the accessible subsystem in another. We characterize their symmetry-constrained structure and define a regime in which a reduced entropy-coherence conservation law holds. We also identify when the induced reduced action on the open system admits a classical interpretation as random frame misalignment, and when it instead reflects quantum reduced-frame effects. We then apply the framework to pure-dephasing dynamics and derive a necessary and sufficient compatibility condition for population preservation. When the frame symmetry commutes with the open system's free Hamiltonian, coherences acquire a multiplicative frame factor, so that locally inferred decoherence rates split into environmental and reference-induced contributions. Ramsey interferometry gives this split a direct operational meaning. Finally, a gravity-motivated dephasing model illustrates how degradation of a phase reference can mimic signatures usually attributed to intrinsic decoherence mechanisms.
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 Schr\"odinger 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 H\"ohn 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 $C|\psi\rangle=0$. 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.
Stefan L. Ludescher, Manuel Mekonnen, Thomas D. Galley et al.· 1 citation
Quantum permutations, or magic unitaries, have in recent years been explored in the context of identifying `genuinely quantum'isometries of graphs. Here, we import this tool in physics, showing that quantum permutations yield a generalisation of quantum reference frames in a discrete setting that is reminiscent of the passage from special to general relativity. We show that the typical quantum reference frames framework corresponds to quantum permutations classified as `classical'in the mathematical literature, and which we demonstrate are quantum controlled transformations (superpositions of classical coordinate maps). Genuinely quantum permutations (i) allow to construct \emph{non--commuting} quantum reference frames (ii) correspond to \emph{local}, as opposed to global, superpositions of transformations. Strikingly, we find that the non-commutativity of quantum fields, when used as reference systems, is exactly what implies that the change of frame is achieved through a genuine quantum permutation. We illustrate the above with several examples in both first and second quantization formalism, which demonstrate (a) simultaneous control on non--commuting variables, (b) the existence of bipartite states that can be localized with a genuine quantum permutation and cannot be localized with the usual quantum reference frame transformations (without introducing additional degrees of freedom), (c) extension of the Ising model symmetries to genuinely quantum permutations, and (d) extension of the symmetries of a scalar field action on curved spacetime to genuinely quantum permutations. While we have in mind applications in quantum gravity, we expect our formalism to be of interest in a wide range of topics in quantum information.
Ofek Bengyat, Č. Brukner, M. Christodoulou· 0 citations
Understanding a composite system through its constituents is a fundamental practice in physics. In the context of quantum reference frames (QRFs), however, combining the usual quantum-theoretic notion of composition with QRF perspectives gives rise to subtle issues, such as the'paradox of the third particle'. Here we study in depth how to compose subsystems in QRF perspectives, building on a recent formalism for QRFs [E.Castro-Ruiz and O.Oreshkov, 2025]. We first show how the frames of external observers can be internalised and treated within the framework. This establishes a consistent hierarchy of QRF perspectives, which we use to define the adding and removing of subsystems. We then explain how, owing to the so-called'extra-particle'degrees of freedom, the formalism gives a consistent treatment of subsystems, avoiding any paradoxes by construction. Consistency then implies that composing subsystems in a QRF perspective differs from, and generalises, the standard quantum-theoretic case. In particular, not every state can be appended in tensor-product form relative to a QRF, and we characterise the set of compatible states. Finally, we introduce'classicalisation', a procedure that recovers a classical-like perspective from a general QRF. This procedure circumvents the aforementioned state restrictions but carries a different operational meaning, which we study through a concrete example.
QBism understands quantum mechanics to be probability theory supplemented by additional nonclassical coherence conditions. In this dissertation, we develop these nonclassical coherence conditions from first principles, emphasizing the role of a well chosen reference measurement. After treating standard probability on subjective Bayesian lines, we demonstrate an equivalence between the QBist approach and the existing framework of generalized probabilistic theories. We show that the fundamental nonclassical coherence relation may almost always be taken to be a gentle modification of the law of total probability, and give a coherentist account of when an experimental scenario has a classical explanation. Finally, we show that when the reference measurement is chosen to correspond to a complex projective 3-design, the shape of quantum state space is implicit in the probabilities which characterize the reference measurement itself. Thus coherence with this single reference measurement, properly understood, implies coherence with all of finite dimensional quantum mechanics. We then attempt a modest reconstruction of quantum theory along these lines, one practical consequence of which is a method for self-testing complex projective $t$-designs for $t\ge 3$ in a theory-agnostic way.
Estimation of work at the quantum scale remains a central challenge in quantum thermodynamics. Canonical approaches have a fundamental drawback: they assume classical control of the quantum system, as implicit in a time-dependent Hamiltonian. Yet the energetic cost of implementing this control is omitted and can exceed the system's energy scale by orders of magnitude, calling into question the operational significance of work values. We address this by autonomizing the controlled energy transfer, embedding the driven dynamics into an energy-conserving evolution on a larger quantum system. Work is then unambiguously identified with the energy transferred between the two systems, singling out a unique observable on the driven system: the work operator. We show that the quantum work operator evades a no-go theorem by deriving a quantum fluctuation theorem that recovers the Jarzynski equality in classical scenarios. We incorporate imperfect control and quantify corrections to work statistics. Extending the framework to open quantum systems, we obtain an operatorial first law in which work, heat, and internal-energy changes are represented by distinct operators on the reduced system. Together, these results settle the long-standing debate over whether work is a quantum observable: it is, once the controlling system is included in the description rather than treated as external.
Carlo Cepollaro, Danial Chughtai, Alberto Spalvieri et al.· 2 citations
The framework of internal quantum reference frames (QRFs) constitutes a universal toolset for dealing with symmetries in quantum theory and has led to new revelations in quantum gravity, gauge theories and foundational physics. Multiple approaches have emerged, sometimes differing in scope and the way symmetries are implemented, raising the question as to their relation. Here, we investigate the relation between three approaches to QRFs for gauge symmetries, namely the
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(PN) approaches. Rather than constructing Hilbert spaces, as the PN approach, the effective approach is based on a quantum phase space parametrized by expectation values and fluctuations, while the emphasis of the algebraic approach is on the state space of complex linear functionals on a kinematical algebra. Nevertheless, external frame information is treated as gauge in all three formalisms, manifested in constraints on states and algebra. We show that these three approaches are, in fact, equivalent for ideal QRFs, distinguished by sharp orientations, which is the previous setting of the first two approaches. Our demonstration pertains to single constraints, including relativistic ones, and encompasses QRF changes. In particular, the QRF transformations of the PN framework agree semiclassically with those of the older effective approach, by which it was inspired. As a physical application, we explore the QRF covariance of uncertainties and fluctuations, which turn out to be frame dependent. This is particularly well-suited for the effective and algebraic approaches, for which these quantities form a natural basis. Finally, we pave the way towards extending these two approaches to non-ideal QRFs by studying the projection and gauge-fixing operations of the Page-Wootters formalism, built into the PN framework, on algebraic states.
J. De Vuyst, Philipp A. Hoehn, Artur Tsobanjan· Quantum· 11 citations
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