Optimal entanglement generation from quantum operations

We consider how much entanglement can be produced by a nonlocal two-qubit unitary operation, $U_{\mathrm{AB}}$—the entangling capacity of $U_{\mathrm{AB}}.$ For a single application of $U_{\mathrm{AB}},$ with no ancillas, we find the entangling capacity and show that it generally helps to act with $U_{\mathrm{AB}}$ on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.