Schematic setup for realizing supercorrelations. HWP1 and HWP2 realize the basis transformation | ↑⟩(| ↓ ⟩) ↔ |H⟩(|V ⟩). HWP3 rotates the photon polarization as |H⟩ ↔ sin θ|H⟩ + cos θ|V ⟩, |V ⟩ ↔ −cos θ|H⟩ + sin θ|V ⟩. The + ϑ represents the cross-Kerr nonlinear interaction between the signal photon and the probe coherent beam, where the signal photon will induce a phase shift + ϑ on the coherent beam |α_1,2⟩_p in the probe mode. |X⟩⟨ X| represents an X quadrature homodyne measurement. PBSi (i = 1, 2, 3, 4, 5) are polarizing beam splitters in {|H⟩, |V ⟩} basis, and PBS6 works in the {|+〉=(1/2)(|H〉+|V〉),|−〉=(1/2)(|H〉−|V〉) } basis.