Speed Limits for Entanglement

TL;DR

This paper establishes a fundamental speed limit for entanglement propagation in relativistic quantum systems, based on thermal equilibrium properties, and supports this with theoretical bounds applicable across various quantum field theories.

Contribution

It introduces a universal bound on entanglement speed derived from relative entropy inequalities, applicable to any relativistic quantum system and supported by holographic and conformal field theory insights.

Findings

Entanglement speed limit set by thermal equilibrium properties.

Bound applies to far-from-equilibrium entanglement dynamics.

Supports a simple physical picture for entanglement propagation.

Abstract

We show that in any relativistic system, entanglement entropy obeys a speed limit set by the entanglement in thermal equilibrium. The bound is derived from inequalities on relative entropy with respect to a thermal reference state. Thus the thermal state constrains far-from-equilibrium entanglement dynamics whether or not the system actually equilibrates, in a manner reminiscent of fluctuation theorems in classical statistical mechanics. A similar shape-dependent bound constrains the full nonlinear time evolution, supporting a simple physical picture for entanglement propagation that has previously been motivated by holographic calculations in conformal field theory. We discuss general quantum field theories in any spacetime dimension, but also derive some results of independent interest for thermal relative entropy in 1+1d CFT.