Quantum state transmission over arbitrarily long distance by pairing coding and quantum repeater

Quantum state is transmitted via noisy channel, the errors introduced by noise will limit the practicality of quantum communication. In this paper, we present a scheme which can overcome this limitation. The central idea is that a quantum bit is paired by another quantum bit to stand for a quantum bit information. This quantum bit pair interacts with the same environment and decoheres collectively. If the range of transmission is not very large, the decoherence of the quantum bit pair can be prevented. If only amplitude damping is considered, our pairing coding can overcome both collective and independent amplitude damping with high probability. Quantum repeater is used to transmit a quantum bit over arbitrarily long distance.