Deterministic Tripartite Entanglement Distributions of the W State over Collective-Noise Channels

A deterministic entanglement distribution protocol (EDP) is proposed in principle for transmitting a maximally entangled W state over collective-noise channels. Using this EDP, a W state can be reconstructed directly from a three-photon entangled state in the frequency degree of freedom prepared among three remote participants due to the fact that it suffers little from the channel noise. In essence, it is a entanglement transformation between different degrees of freedom in three-photon entangled system. This EDP adopts the cross-Kerr nonlinearity media to complete the task of the single-photon detections, which can increase the efficiency of entanglement distribution since it does not require the sophisticated single-photon detectors for the usual measurements and the retained photons can be still held solely by three respective participants after entanglement distillation.