Controlled Implementation of Non-local CNOT Operation Using Three-Qubit Entanglement

We investigate the controlled implementation of a non-local CNOT operation using a three-qubit entangled state. Firstly, we show how the non-local CNOT operation can be implemented with unit fidelity and unit probability by using a maximally entangled GHZ state as controlled quantum channel. Then, we put forward two schemes for conclusively implementing the non-localoperation with unit fidelity by employing a partially entangled pure GHZstate as quantum channel. The feature of these schemes is that a thirdside is included, who may participate the process of quantum non-localimplementation as a supervisor. Furthermore, when the quantum channel ispartially entangled, the third one can rectify the state distorted byimperfect quantum channel. In addition to the GHZ class state, the W classstate can also be used to implement the same non-local operationprobabilistically. The probability of successful implementation using the Wclass state is always less than that using the GHZ class state.