Feasible preparation of polarization hybrid Greenberger-Horne-Zeilinger state based on optimal quantum scissors

Hybrid entanglement containing continuous-variable (CV) and discrete-variable quantum systems combines the advantages of both systems. The polarization hybrid entanglement has been widely applied in various quantum information processing tasks. In this paper, we propose the preparation protocols for two kinds of polarization hybrid Greenberger-Horne-Zeilinger (GHZ) states using the optimal quantum scissors (QSs) based on the local-quadrature squeezing operation. Our protocols first use the cat states and the coherent states as resources to deterministically generate the polarization CV GHZ states, and then use the optimal QSs to truncate the coherent states to generate two kinds of polarization hybrid GHZ states. Our preparation protocols have some advantages. First, they only require the linear optical elements, especially the practical "on-off" photon detectors, so that they are feasible and flexible under current experimental conditions. Second, they do not reply on the post-selection. The generated polarization hybrid GHZ states can be remained for other applications. Third, the optimal QS can effectively increase the fidelity of the target hybrid GHZ states. Our preparation protocols have application potential in future quantum information processing field with hybrid entanglement.