Entanglement Rates and the Stability of the Area Law for the Entanglement Entropy

TL;DR

This paper proves an upper bound on entanglement rates for local Hamiltonians and demonstrates the stability of the area law for entanglement entropy in quantum spin systems during adiabatic evolutions.

Contribution

It establishes a proven upper bound on entanglement rates and confirms the stability of the area law under certain quantum evolutions.

Findings

Proved a conjecture by Bravyi on entanglement rate bounds.

Showed the area law remains stable during adiabatic evolutions.

Provided theoretical foundations for entanglement behavior in quantum systems.

Abstract

We prove a conjecture by Bravyi on an upper bound on entanglement rates of local Hamiltonians. We then use this bound to prove the stability of the area law for the entanglement entropy of quantum spin systems under adiabatic and quasi-adiabatic evolutions.