Efficient Polarization Entanglement Purification Using Spatial Entanglement

The protocol using spatial entanglement to purify polarization entanglement by entanglement transformation between different degrees of freedom in a realistic environment is elaborated. Our analyses show that the bit-flip error can be completely purified, but the pure maximally entangled state can not be obtained ultimately if the spatial entanglement is impure. The fidelity of the purified state is decided by the spatial entanglement. Furthermore, this protocol can also be extended to purify the multi-particle Greenberg—Horne—Zeilinger （GHZ） state. It is presented that the spatial entanglement can be served as another source to improve the quality of entanglement.