Quantum reference frames for general symmetry groups

Abstract

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 $G=N⋊P$ 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.

arXiv comment22 pages, 7 figures

References in corpus (27)

• Relational Quantum Mechanics
• Reference frames, superselection rules, and quantum information
• The resource theory of quantum reference frames: manipulations and monotones
• How Quantum Mechanics can consistently describe the use of itself
• Quantum theory cannot consistently describe the use of itself
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• What is quantum mechanics trying to tell us?
• Superselection rules and quantum protocols
• Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
• Switching internal times and a new perspective on the 'wave function of the universe'
• Quantum communication using a bounded-size quantum reference frame
• Physics within a quantum reference frame
• Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics
• Dialogue Concerning Two Views on Quantum Coherence: Factist and Fictionist
• Changing quantum reference frames
• How to switch between relational quantum clocks
• Toy Model for a Relational Formulation of Quantum Theory
• Dynamics of a Quantum Reference Frame
• Macroscopic superpositions require tremendous measurement devices
• Relativity of Quantum States and Observables
• Approximating relational observables by absolute quantities: A quantum accuracy-size trade-off
• Quantum reference frames associated with non-compact groups: the case of translations and boosts, and the role of mass
• Kinematics and dynamics in noninertial quantum frames of reference
• Galilei covariance and Einstein's equivalence principle in quantum reference frames
• Quantum Reference Frames and Their Applications to Thermodynamics

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