Probabilistic Implementation of Non-Local CNOT Operation and Entanglement Purification

We propose a protocol for implementation of nonlocal CNOT operation using a partially entangled channel and show that when partially entangled pairs are taken as quantum channels, the nonlocal CNOT operation can be implemented probabilistically by introducing a collective unitary transformation. The required resources for implementation of the nonlocal CNOT operation in this case are discussed. We also point out that the nonlocal CNOT operation can be used as a puritlcation protocol to concentrate entanglement from an ensemble of partially entangled particles into a subensemble of maximally entanglement ones.