  Nonlocal gate operation is based on sharing an ancillary pair of qubits in
perfect entanglement. When the ancillary pair are partially entangled, the
efficiency of the gate operation drops. Using general transformations, we
devise probabilistic nonlocal gates, which perform the nonlocal operation
conclusively when the ancillary pair are only partially entangled. We show that
a controlled purification protocol can be implemented by the probabilistic
nonlocal operation.
