Linear-optical heralded amplification protocol for two-photon spatial-mode-polarization hyperentangled state

Hyperentanglement can enlarge the capacity of quantum channel and has big potential application in long-distance quantum communication. However, the channel noise may cause photon transmission loss, which largely limits the practical application of hyperentanglement. In the paper, we propose a linear-optical heralded amplification protocol for protecting the two-photon spatial-mode-polarization hyperentangled state. Our protocol can effectively increase the fidelity of the hyperentangled state while preserve its encoded spatial and polarization features. Comparing with previous heralded amplification protocol for the spatial-mode-polarization hyperentangled state, our protocol is easier to be implemented under current experimental condition. Moreover, besides amplification, if necessary, our protocol can adjust the entanglement coefficients in both polarization and spatial-mode degrees of freedom of the distilled hyperentangled state and recover the less-entangled hyperentangled state into the maximally entangled state. Based on above features, our protocol gives a possible solution to overcome the photon loss and decoherence problems occurred in practical noisy quantum channel condition.