Optimizing local protocols for implementing bipartite nonlocal unitary gates using prior entanglement and classical communication

We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and they are deterministic while also being 'one-shot', in that they use only one copy of an entangled resource state. The optimization minimizes the amount of entanglement needed, and also the amount of classical communication, and it is often the case that less of each of these resources is needed than with an alternative protocol using two-way teleportation.