Internal quantum reference frames for finite Abelian groups

Abstract

Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained treatment of such quantum reference frames (QRFs) for the case when the underlying configuration space is a finite Abelian group, significantly extending our previous work (Quantum 5, 530 (2021)). The simplicity of this setup admits a fully rigorous quantum information-theoretic analysis, while maintaining sufficient structure for exploring many of the conceptual and structural questions also pertinent to more complicated setups. We exploit this to derive several important structures of constraint quantization with quantum information-theoretic methods and to reveal the relation between different approaches to QRF covariance. In particular, we characterize the "physical Hilbert space" -- the arena of the "perspective-neutral" approach -- as the maximal subspace that admits frame-independent descriptions of purifications of states. We then demonstrate the kinematical equivalence and, surprising, dynamical inequivalence of the "perspective-neutral" and the "alignability" approach to QRFs. While the former admits unitaries generating transitions between arbitrary subsystem relations, the latter, remarkably, admits no such dynamics when requiring symmetry-preservation. We illustrate these findings by example of interacting discrete particles, including how dynamics can be described "relative to one of the subsystems".

arXiv comment22 pages, 1 figure. V2: close to published version

References in corpus (64)

• Reference frames, superselection rules, and quantum information
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Informational derivation of Quantum Theory
• Catalytic Coherence
• Quantum coherence, time-translation symmetry and thermodynamics
• Quantum Theory From Five Reasonable Axioms
• The resource theory of quantum reference frames: manipulations and monotones
• Local subsystems in gauge theory and gravity
• Remarks on entanglement entropy for gauge fields
• A derivation of quantum theory from physical requirements
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Partial and Complete Observables for Canonical General Relativity
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• The Trinity of Relational Quantum Dynamics
• Edge modes of gravity -- I: Corner potentials and charges
• Quantum Time
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• Autonomous quantum clocks: does thermodynamics limit our ability to measure time?
• Why Gauge?
• Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
• Relational Observables in Gravity: a Review
• Quantizing time: Interacting clocks and systems
• Quantum clocks observe classical and quantum time dilation
• Switching internal times and a new perspective on the 'wave function of the universe'
• Physics within a quantum reference frame
• Equivalence of approaches to relational quantum dynamics in relativistic settings
• Quantum reference frames for general symmetry groups
• Relativistic quantum reference frames: the operational meaning of spin
• Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics
• New boundary variables for classical and quantum gravity on a null surface
• Changing quantum reference frames
• Spacetime Quantum Reference Frames and superpositions of proper times
• How to switch between relational quantum clocks
• Coherence and asymmetry cannot be broadcast
• Quantum Relativity of Subsystems
• Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Fock representation of gravitational boundary modes and the discreteness of the area spectrum
• Edge modes as reference frames and boundary actions from post-selection
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Extended actions, dynamics of edge modes, and entanglement entropy
• Relativity of Quantum States and Observables
• Approximating relational observables by absolute quantities: A quantum accuracy-size trade-off
• Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach
• Quantum reference frames associated with non-compact groups: the case of translations and boosts, and the role of mass
• Construction of quantum Dirac observables and the emergence of WKB time
• A Unified Geometric Framework for Boundary Charges and Particle Dressings
• Toolbox for reconstructing quantum theory from rules on information acquisition
• The group structure of dynamical transformations between quantum reference frames
• Relativistic Bell Test within Quantum Reference Frames
• Observer-dependent locality of quantum events
• Relational observables, reference frames, and conditional probabilities
• Noncausal Page-Wootters circuits
• Transformation of Spin in Quantum Reference Frames
• An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
• Quantum resource covariance
• Communicating without shared reference frames
• A relational perspective on the Wigner-Araki-Yanase theorem
• Edge modes without edge modes
• Einstein's Equivalence principle for superpositions of gravitational fields and quantum reference frames
• Perspective-neutral approach to quantum frame covariance for general symmetry groups

Cited by in corpus (20)

• Edge modes as reference frames and boundary actions from post-selection
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Edge modes as dynamical frames: charges from post-selection in generally covariant theories
• Quantum reference frames for an indefinite metric
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Entanglement-asymmetry correspondence for internal quantum reference frames
• Inference of gravitational field superposition from quantum measurements
• Watching the Clocks: Interpreting the Page-Wootters Formalism and the Internal Quantum Reference Frame Programme
• Quantum Reference Frames for Lorentz Symmetry
• Robustness of the Page-Wootters construction across different pictures, states of the universe and system-clock interactions
• Quantum generalisation of Einstein's Equivalence Principle can be verified with entangled clocks as quantum reference frames
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Minimal Areas from Entangled Matrices
• Long-time Quantum Scrambling and Generalized Tensor Product Structures
• Searching for a physical description relative to a quantum system
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Quantum Galilei group as quantum reference frame transformations
• What can we do in a symmetry-constrained perspective? The importance of the total charge's status in quantum reference frame frameworks
• Energy Cost of Localization of Relational Quantum Information