  Logic-qubit entanglement has attracted much attention in both quantum
communication and quantum computation. Here, we present an efficient protocol
to distill the logic-qubit entanglement with the help of cross-Kerr
nonlinearity. This protocol not only can purify the logic bit-flip error and
logic phase-flip error, but also can correct the physical bit-flip error
completely. We use cross-Kerr nonlinearity to construct quantum nondemolition
detectors. Our distillation protocol for logic-qubit entanglement may be useful
for the practical applications in quantum information, especially in
long-distance quantum communication.
