Perfect distribution of four-photon χ-typeχ-type entangled states over an arbitrary collective noise channel by spatial degree of freedom

A quantum entanglement distribution protocol of a four-photon χ-typeχ-type polarization-entangled state is presented by exploiting spatial degree of freedom, which is immune to an arbitrary collective noise. This protocol can be fulfilled with nearly unitary probability by the assistance of Homodyne measurement (Y quadrature measurement) that determines the polarization part of the four photons in the transmitted process. Transforming the polarization entanglement mode to spatial entanglement mode and back, the distribution of this entangled state can overcome the influence of collective noise. Moreover, the combination of currently available optical elements is exploited in this protocol, which includes polarization beam splitters, reflection mirrors, optical detectors, and half wave plates functioning as the NOT gates, etc.