Entanglement capabilities of non-local Hamiltonians

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Abstract
We analyze the entanglement capability of an arbitrary non-local Hamiltonian H acting on two qubits. We use the entanglement rate \Gamma, namely the entanglement produced per time step \delta t during the corresponding non-local evolution, to quantify the entanglement production of H. This quantity depends on the initial state of the two-qubit system. For an arbitrary Hamiltonian, we explicitly calculate the state which maximizes \Gamma. It turns out to be advantageous to start with some entanglement rather than with a product state. Remarkably, we find that the optimal initial entanglement is independent of the Hamiltonian. We also show that allowing for local ancillas helps to further increase the entanglement rate \Gamma for certain kinds of Hamiltonians.

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