Probabilistic implementation of a nonlocal operation using a nonmaximally entangled state

We develop the probabilistic implementation of a nonlocal gate exp[i xi sigma(nA)sigma(nB)] and xi is an element of[0,(pi/4)], by using a single nonmaximally entangled state. We prove that nonlocal gates can be implemented with a fidelity of >79.3% and a consumption of < 0.969 ebits and two classical bits, when xi <= 0.353. This provides a higher bound for the feasible operation compared to the former techniques. Besides, gates with xi >= 0.353 can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency as the distillation-based protocol, while our method saves extra classical resources. Gates with xi -> 0 can be implemented with nearly unit probability and a small entanglement. We also generalize some applications to the multiple system, where we find it is possible to implement certain nonlocal gates between many nonentangled partners using a nonmaximally multiple entangled state.