Entanglement capability of a self-inverse Hamiltonian evolution

We determine the entanglement capability of a self-inverse Hamiltonian evolution, which reduces to the known result for the Ising Hamiltonian, and identify optimal input states for yielding the maximal entanglement rate. We introduce the concept of the operator entanglement rate, and find that the maximal operator entanglement rate gives a lower bound on the entanglement capability of a general Hamiltonian.