Universal entanglement timescale for R\'enyi entropies

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.