On the efficiency of nonlocal gates generation

We propose and study a method for using non-maximally entangled states to implement probabilistically non-local gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequences, the method becomes more efficient at a certain range of parameters. Gates of the form $\exp[i\xi\sigma_{n_A}\sigma_{n_B}]$ with $\xi\ll1$, can be implemented with nearly unit probability and with vanishingly small entanglement, while for the distillation-based method the gate is produced with a vanishing success probability. We also derive an upper bound to the optimal success probability and show that in the small entanglement limit, the bound is tight.