Deterministic state analysis for polarization-spatial-time-bin hyperentanglement with nonlinear optics

Abstract

We present two deterministic hyperentangled state analysis protocols for photons entangled in polarization, spatial-mode and time-bin degrees of freedom (DOFs). The first protocol is a hyperentangled Bell state analyzer, and the second is a hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analyzer for three photons. In the first scheme, we construct a polarization parity-check quantum nondemolition detector (P-QND) and a spatial-mode parity-check quantum nondemolition detector (S-QND) based on cross-Kerr nonlinearities. With these P-QND and S-QND, we design the setup of Bell state analyzer in polarization and spatial-mode DOFs. While time-bin entanglement is discriminated with the help of the polarization entanglement. We generalize the idea to analyze the three-photon hyperentangled GHZ states. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely discriminated via three steps. These two state analysis schemes are expected to provide practical applications for high-capacity and long-distance quantum communication.