Entanglement-asymmetry correspondence for internal quantum reference frames

Abstract

In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time-dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S. Surprisingly, this duality holds exactly regardless of the choice of coherent state system used to condition on the reference frame. Averaging asymmetry over all conditional states, we obtain a simple representation-theoretic expression that admits the study of the quality of imperfect quantum reference frames, quantum speed limits for imperfect clocks, and typicality of asymmetry in a unified way. Our results shed light on the role of entanglement for establishing asymmetry in a fully symmetric quantum world.

5+8 pages, 2 figures. v3: some minor clarifications and simplifications. Close to published version

References in corpus (20)

• Reference frames, superselection rules, and quantum information
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Aspects of generic entanglement
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Quantum superposition of spacetimes obeys Einstein's Equivalence Principle
• Equivalence of approaches to relational quantum dynamics in relativistic settings
• Quantum reference frames for general symmetry groups
• Spacetime Quantum Reference Frames and superpositions of proper times
• Quantum Relativity of Subsystems
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• The group structure of dynamical transformations between quantum reference frames
• Relativistic Bell Test within Quantum Reference Frames
• Internal quantum reference frames for finite Abelian groups
• Transformation of Spin in Quantum Reference Frames
• Communicating without shared reference frames
• A relational perspective on the Wigner-Araki-Yanase theorem
• Quantifying resources for Page-Wootters mechanism: Shared asymmetry as relative entropy of entanglement

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• Indefinite causal order and quantum coordinates