Abstract
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.