Universal Bounds on the Time Evolution of Entanglement Entropy

TL;DR

This paper derives universal bounds on how quickly entanglement entropy can change over time in relativistic quantum field theories, applicable to various states and spacetime geometries.

Contribution

It introduces a general method using relative entropy to establish bounds on entanglement entropy evolution across different theories and conditions.

Findings

Bounds are applicable to both mixed and pure states.

The bounds can be extended to curved spacetime.

Illustrative examples demonstrate the bounds' utility.

Abstract

Using relative entropy, we derive bounds on the time rate of change of geometric entanglement entropy for any relativistic quantum field theory in any dimension. The bounds apply to both mixed and pure states, and may be extended to curved space. We illustrate the bounds in a few examples and comment on potential applications and future extensions.