Universal entanglement timescale for R\'enyi entropies

TL;DR

This paper demonstrates that a universal timescale governs the growth of all Re9nyi entropies during entanglement development in bipartite quantum systems, depending only on the initial state and the interaction Hamiltonian.

Contribution

It extends the concept of a universal entanglement timescale to all Re9nyi entropies, providing a comprehensive characterization of bipartite entanglement growth.

Findings

The timescale is universal for all Re9nyi entropies.

The timescale depends solely on the initial state and the interaction Hamiltonian.

It applies to any Hamiltonian and initial state in bipartite systems.

Abstract

Recently it was shown that the growth of entanglement in an initially separable state, as measured by the purity of subsystems, can be characterized by a timescale that takes a universal form for any Hamiltonian. We show that the same timescale governs the growth of entanglement for all R\'enyi entropies. Since the family of R\'enyi entropies completely characterizes the entanglement of a pure bipartite state, our timescale is a universal feature of bipartite entanglement. The timescale depends only on the interaction Hamiltonian and the initial state.