Implementing nonlocal gates with nonmaximally entangled states

We propose and study a method for using nonmaximally entangled states to probabilistically implement desired nonlocal gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequence, the method becomes more efficient at a certain range of parameters. Gates of the form exp[iξσ _nAσ _nB] with ξ≪1 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.