arXiv subjects

Thomas D. Galley

Publications and source records attributed to Thomas D. Galley.

At least 19 recordsLinked to original sources

arXiv2026

Quantum reference frames beyond subsystems: a reconstruction and generalization of the perspective-neutral framework

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 $C|ψ\rangle=0$. 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.

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arXiv2026

Complete Relational Description of Spin in a Quantum Background

The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions -- a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to \emph{two} large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.

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arXiv2026

Gravity-mediated entanglement via infinite-dimensional systems

There has been a wave of recent interest in detecting the quantum nature of gravity with table-top experiments that witness gravitationally mediated entanglement. Central to these proposals is the assumption that any mediator capable of generating entanglement must itself be nonclassical. However, previous arguments for this have modelled classical mediators as finite, discrete systems such as bits, which excludes physically relevant continuous and infinite-dimensional systems such as those of classical mechanics and field theory. In this work, we close this gap by modelling classical systems as commutative unital C*-algebras, arguably encompassing all potentially physically relevant classical systems. We show that these systems cannot mediate entanglement between two quantum systems A and B, even if A and B are themselves infinite-dimensional or described by arbitrary unital C*-algebras (as in Quantum Field Theory), composed with an arbitrary C*-tensor product. This result reinforces the conclusion that the observation of gravity-induced entanglement would require the gravitational field to possess inherently non-classical features.

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arXiv2026

Invariance under quantum permutations rules out parastatistics

Quantum systems invariant under particle exchange are either Bosons or Fermions, even though quantum theory in principle admits more general behavior under permutations. But why do we not observe such paraparticles in nature? The analysis of this question was previously limited primarily to specific quantum field theory models. Here we give two distinct model-independent arguments that rule out parastatistics, i.e. fundamentally indistinguishable quantum systems transforming under higher-dimensional representations of the symmetric group, which draw on quantum information theory and recent research on internal quantum reference frames. First, we introduce a notion of complete invariance: quantum systems should not only preserve their local state under permutations, but also the quantum information they carry about other systems, in analogy to the notion of complete positivity in quantum information theory. Second, we demand that quantum systems are invariant under quantum permutations, i.e. permutations conditioned on values of permutation-invariant observables. For both, we show that the respective principle is fulfilled if and only if the particle is a Boson or Fermion. Our results show how quantum reference frames can shed light on a longstanding problem of quantum physics, they underline the crucial role played by the compositional structure of quantum information, and demonstrate the explanatory power but also subtle limitations of recently proposed quantum covariance principles.

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arXiv2026

Resource-theoretic hierarchy of contextuality for general probabilistic theories

In this work we present a hierarchy of generalized contextuality. It refines the traditional binary distinction between contextual and noncontextual theories, and facilitates their comparison based on how contextual they are. Our approach focuses on the contextuality of prepare-and-measure scenarios, described by general probabilistic theories (GPTs). To motivate the hierarchy, we define it as the resource ordering of a novel resource theory of GPT-contextuality. The building blocks of its free operations are classical systems and univalent simulations between GPTs. These simulations preserve operational equivalences and thus cannot generate contextuality. Noncontextual theories can be recovered as least elements in the hierarchy. We then define a new contextuality monotone, called classical excess, given by the minimal error of embedding a GPT within an infinite classical system. In addition, we show that the optimal success probability in the parity oblivious multiplexing game also defines a monotone in our resource theory. Finally, we discuss whether the non-free operations can be understood as implementing information erasure and thus explaining the fine-tuning aspect of contextuality.

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arXiv2026

Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality

Characterizing the nonclassicality of quantum systems under minimal assumptions is an important challenge for quantum foundations and technology. Here we introduce a theory-independent method of process tomography and perform it on a superconducting qubit. We demonstrate its decoherence without assuming quantum theory or trusting the devices by modelling the system as a general probabilistic theory. We show that the superconducting system is initially well-described as a quantum bit, but that its realized state space contracts over time, which in quantum terminology indicates its loss of coherence. The system is initially nonclassical in the sense of generalized contextuality: it does not admit of a hidden-variable model where statistically indistinguishable preparations are represented by identical hidden-variable distributions. In finite time, the system becomes noncontextual and hence loses its nonclassicality. Moreover, we demonstrate in a theory-independent way that the system undergoes non-Markovian evolution at late times. Our results extend theory-independent tomography to time-evolving systems, and show how important dynamical physical phenomena can be experimentally monitored without assuming quantum theory.

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arXiv2025

Symmetry-induced failures of tomographic locality: Constructing foil theories by twirling

Tomographic locality is a principle commonly used in the program of finding axioms that pick out quantum theory within the landscape of possible theories. The principle asserts the sufficiency of local measurements for achieving a tomographic characterization of any bipartite state. In this work, we explore the meaning of the principle of tomographic locality by developing a simple scheme for generating a wide variety of theories that violate the principle. In this scheme, one starts with a tomographically local theory -- which can be classical, quantum or post-quantum -- and a physical symmetry, and one restricts the processes in the theory to all and only those that are covariant with respect to the collective action of that symmetry. We refer to the resulting theories as twirled worlds. We show that failures of tomographic locality are ubiquitous in twirled worlds. From the possibility of such failures in classical twirled worlds, we argue that the failure of tomographic locality (i.e., tomographic nonlocality) does not imply ontological holism. Our results also demonstrate the need for researchers seeking to axiomatize quantum theory to take a stand on the question of whether there are superselection rules that have a fundamental status.

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arXiv2025

Interpreting quantum reference frame transformations through a simple example

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 $\mathbb{Z}_2$ 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 operational meaning of each approach and the contexts in which they may be most naturally applied.

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arXiv2025

Response to "The measurement postulates of quantum mechanics are not redundant"

Adrian Kent has recently presented a critique [arXiv:2307.06191] of our paper [Nat. Comms. 10, 1361 (2019)] in which he claims to refute our main result: the measurement postulates of quantum mechanics can be derived from the rest of postulates, once we assume that the set of mixed states of a finite-dimensional Hilbert space is finite-dimensional. To construct his argument, Kent considers theories resulting from supplementing quantum mechanics with hypothetical "post-quantum" measurement devices. We prove that each of these theories contains pure states (i.e. states of maximal knowledge) which are not rays of the Hilbert space, in contradiction with the "pure state postulate" of quantum mechanics. We also prove that these alternatives violate the finite-dimensionality of mixed states. Each of these two facts separately invalidates the refutation. In this note we also clarify the assumptions used in [Nat. Comms. 10, 1361 (2019)] and discuss the notions of pure state, physical system, and the sensitivity of the structure of the state space under modifications of the measurements or the dynamics.

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arXiv2024

Spin-bounded correlations: rotation boxes within and beyond quantum theory

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2,2,2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes.

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arXiv2023

Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible

When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principles of quantum theory or general relativity, but it is usually hard to assess which one without resorting to a specific model. Here, we answer this question in a theory-independent way using General Probabilistic Theories (GPTs). We consider the interactions of the gravitational field with a single matter system, and derive a no-go theorem showing that when gravity is classical at least one of the following assumptions needs to be violated: (i) Matter degrees of freedom are described by fully non-classical degrees of freedom; (ii) Interactions between matter degrees of freedom and the gravitational field are reversible; (iii) Matter degrees of freedom back-react on the gravitational field. We argue that this implies that theories of classical gravity and quantum matter must be fundamentally irreversible, as is the case in the recent model of Oppenheim et al. Conversely if we require that the interaction between quantum matter and the gravitational field is reversible, then the gravitational field must be non-classical.

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arXiv2023

A no-go theorem on the nature of the gravitational field beyond quantum theory

Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.

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arXiv2022

Reply to "Masanes-Galley-Müller and the State-Update Postulate"

In a recent comment on the arXiv, Blake C. Stacey criticizes our derivation of the quantum state update rule in Nat. Commun. 10, 1361 (2019). Here we argue that the criticism is unfounded. In particular, and in contrast to Stacey's claims, our proof does not assume linearity.

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arXiv2022

Post-quantum steering is a stronger-than-quantum resource for information processing

We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing -- remote state preparation. In addition, we show that the phenomenon of post-quantum steering is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond quantum theory, hence making its study fundamentally relevant. We show these results by formulating a new compositional general probabilistic theory -- which we call Witworld -- with strong post-quantum features, which proves to be a intuitive and useful tool for exploring steering and its applications beyond the quantum realm.

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arXiv2022

Quantum Relativity of Subsystems

One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. We further demonstrate that subalgebras which commute before imposing the symmetry constraint can translate into non-commuting algebras in a given QRF perspective after symmetry imposition. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.

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arXiv2021

Perspective-neutral approach to quantum frame covariance for general symmetry groups

In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. Here, we extend the perspective-neutral approach to QRF covariance to general unimodular Lie groups. This is a framework that links internal QRF perspectives via a manifestly gauge-invariant Hilbert space in the form of "quantum coordinate transformations", and we clarify how it is a quantum extension of special covariance. We model the QRF orientations as coherent states which give rise to a covariant POVM, furnishing a consistent probability interpretation and encompassing non-ideal QRFs whose orientations are not perfectly distinguishable. We generalize the construction of relational observables, establish a variety of their algebraic properties and equip them with a transparent conditional probability interpretation. We import the distinction between gauge transformations and physical symmetries from gauge theories and identify the latter as QRF reorientations. The "quantum coordinate maps" into an internal QRF perspective are constructed via a conditioning on the QRF's orientation, generalizing the Page-Wootters formalism and a symmetry reduction procedure. We find two types of QRF transformations: gauge induced "quantum coordinate transformations" as passive unitary changes of description and symmetry induced active changes of relational observables from one QRF to another. We reveal new effects: (i) QRFs with non-trivial orientation isotropy groups can only resolve isotropy-group-invariant properties of other subsystems; (ii) in the absence of symmetries, the internal perspective Hilbert space "rotates" through the kinematical subsystem Hilbert space as the QRF changes orientation. Finally, we invoke the symmetries to generalize the quantum relativity of subsystems before comparing with other approaches. [Abridged]

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arXiv2021

How dynamics constrains probabilities in general probabilistic theories

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with the action of the reversible dynamics, whilst the probabilistic structure determines the measurements and the outcome probabilities. For transitive dynamical structures whose dynamical group and stabiliser subgroup form a Gelfand pair we show that all probabilistic structures are rigid (cannot be infinitesimally deformed) and are in one-to-one correspondence with the spherical representations of the dynamical group. We apply our methods to classify all probabilistic structures when the dynamical structure is that of complex Grassmann manifolds acted on by the unitary group. This is a generalisation of quantum theory where the pure states, instead of being represented by one-dimensional subspaces of a complex vector space, are represented by subspaces of a fixed dimension larger than one. We also show that systems with compact two-point homogeneous dynamical structures (i.e. every pair of pure states with a given distance can be reversibly transformed to any other pair of pure states with the same distance), which include systems corresponding to Euclidean Jordan Algebras, all have rigid probabilistic structures.

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arXiv2020

Quantum reference frames for general symmetry groups

A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational formalism which identifies coordinate systems with elements of a symmetry group $G$, we define a general operator for reversibly changing between quantum reference frames associated to a group $G$. This generalises the known operator for translations and boosts to arbitrary finite and locally compact groups, including non-Abelian groups. We show under which conditions one can uniquely assign coordinate choices to physical systems (to form reference frames) and how to reversibly transform between them, providing transformations between coordinate systems which are `in a superposition' of other coordinate systems. We obtain the change of quantum reference frame from the principles of relational physics and of coherent change of reference frame. We prove a theorem stating that the change of quantum reference frame consistent with these principles is unitary if and only if the reference systems carry the left and right regular representations of $G$. We also define irreversible changes of reference frame for classical and quantum systems in the case where the symmetry group $G$ is a semi-direct product $G = N \rtimes P$ or a direct product $G = N \times P$, providing multiple examples of both reversible and irreversible changes of quantum reference system along the way. Finally, we apply the relational formalism and changes of reference frame developed in this work to the Wigner's friend scenario, finding similar conclusions to those in relational quantum mechanics using an explicit change of reference frame as opposed to indirect reasoning using measurement operators.

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