Entanglement-asymmetry correspondence for internal quantum reference frames

TL;DR

This paper establishes a precise relationship between entanglement and asymmetry in quantum reference frames, providing a unified framework to analyze imperfect clocks, quantum speed limits, and asymmetry typicality in symmetric quantum systems.

Contribution

It introduces an exact duality between entanglement and asymmetry for internal quantum reference frames, applicable to arbitrary symmetry groups and independent of coherent state choices.

Findings

Exact entanglement-asymmetry correspondence for quantum reference frames.

Representation-theoretic expression for asymmetry averaging.

Insights into quantum speed limits and typicality of asymmetry.

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.