Fig. 1. Schematic of preparing the hybrid entangled state. A small fraction of an even cat state |cat+⟩ is tapped by a BS, and then is coupled on a PBS with a vertical-polarization single photon. Each click event at the output of the DV part heralds the generation of the polarization-cat hybrid entangled state. BS, beam-splitter; PBS, polarization beam-splitter.

Fig. 2. Theoretical predictions of entanglement and quantum coherence of the hybrid state. (a) Logarithmic negativity and l1-norm of the hybrid state as a function of the probability of horizontal-polarization photon. (b) Dependence of logarithmic negativity and l1-norm of the hybrid state on the transmission efficiency in the CV and DV lossy channels. Dashed and solid curves represent logarithmic negativity and l1-norm of the hybrid state when the loss exists in DV and CV parts, respectively.

Fig. 3. Experimental setup for the preparation of the polarization-cat hybrid entangled state. SHG, second harmonic generator; OPA, optical parameter amplifier; IF, interference filter; FC, filter cavity; AOMs, acousto-optic modulators; AMs, amplitude modulators; HWP, half-wave plate; QWP, quarter-wave plate; PPKTP, periodically poled KTiOPO4; PBS, polarization beam-splitter; APD, avalanche photodiode; HD, homodyne detector; LO, local oscillator.

Fig. 4. The reconstructed Wigner functions of the CV part of the polarization-cat hybrid entangled state when the DV part is projected onto the six polarization bases. (a) Wigner functions; (b) contour plots in phase space. All results are corrected for a detection efficiency of 80%.

Fig. 5. (a) Wigner functions of the hybrid entangled state associated with the reduced density matrices ⟨m|ρ^|n⟩, where m,n∈{H,V}. The two conjugated off-diagonal terms placed on the right and left corners are plotted according to the real and imaginary parts of the corresponding Wigner functions, respectively. (b) The density matrix of experimentally obtained hybrid entangled state in the bases of polarization and cat state.

Fig. 6. The periodic timing of the whole system in our experiment.