Emergent classical gauge symmetry from quantum entanglement

TL;DR

This paper explains how quantum entanglement can lead to emergent classical gauge symmetries, with a general mechanism demonstrated through toy models and potential implications for gravity.

Contribution

It provides a precise characterization of when quantum subsystems can be treated classically, linking entanglement structure to emergent gauge symmetries and classical degrees of freedom.

Findings

Entanglement structures impose strong constraints on classical states.

Emergent gauge symmetries can be understood via local descriptions with appropriate gauging.

Evidence suggests a role in the emergence of bulk diffeomorphism invariance in gravity.

Abstract

We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterisation of when it is consistent to treat a quantum subsystem classically in such a limit, namely: in any quantum state corresponding to a definite classical state in the classical limit, the reduced density matrix of the subsystem must be approximately proportional to a projection operator, and the projection operators for different classical subsystem states must obey an approximate mutual orthogonality condition. These are strong constraints on the entanglement structure of classical states. They generically give rise to fundamentally non-local classical degrees of freedom, which may nevertheless be accounted for using a completely local kinematical description, if one gauges this description in the right way. The mechanism we describe is very general, but for concreteness we exhibit a toy example involving three entangled spins at high angular momentum, and we also describe a significant group-theoretic generalisation of this toy example. Finally, we give evidence that this phenomenon plays a role in the emergence of bulk diffeomorphism invariance in gravity.