Entanglement rates and area laws

TL;DR

This paper establishes an optimal upper bound on entanglement generation rates by Hamiltonians and connects area laws for entanglement entropy to quantum phases in many-body systems.

Contribution

It provides a new exponential improvement on bounds for entanglement rates and links area laws to phase equivalence in quantum many-body systems.

Findings

Derived an optimal bound on entanglement growth rates.

Proved that area laws are preserved within quantum phases.

Connected entanglement entropy bounds to phase transitions.

Abstract

We prove an upper bound on the maximal rate at which a Hamiltonian interaction can generate entanglement in a bipartite system. The scaling of this bound as a function of the subsystem dimension on which the Hamiltonian acts nontrivially is optimal and is exponentially improved over previously known bounds. As an application, we show that a gapped quantum many-body spin system on an arbitrary lattice satisfies an area law for the entanglement entropy if and only if any other state with which it is adiabatically connected (i.e. any state in the same phase) also satisfies an area law.