Fig. 1. (a) Illustration of the decoherence process of optical cat state in phase space. An ideal optical odd cat state with amplitude α=1 transmits through a lossy channel with transmission efficiency of 50%, and the Wigner functions are displayed before and after transmission. (b) Experimental setup. A lossy channel consists of a half-wave plate (HWP) and a polarization beam splitter (PBS). OPA, optical parameter amplification with cavity length of 480 mm; SHG, second harmonic generator with cavity length of 480 mm; IF, interference filter (0.4 nm); FC, filter cavity with cavity length of 0.75 mm; FC2, filter cavity with cavity length of 2.05 mm; HD, homodyne detector; LO, local oscillator; APD, avalanche photodiode.

Fig. 2. Experimental results. (a)–(d) Wigner functions W(x,p), (e)–(h) projections, and (i)–(l) absolute values of the density matrix elements in the Fock basis when the transmission efficiencies are 100%, 80%, 60%, and 40%, respectively. All the results are corrected for 80% detection efficiency. Only the subspace up to seven photons is shown.

Fig. 3. Dependence of relative entropy, l1 norm, fidelity, and negativity of cat states on the transmission efficiency. The red solid curve and black dashed curve correspond to the experimentally prepared cat state and the ideal cat state, respectively. The blue dots represent the experimental results.

Fig. 4. Dependence of relative entropy and l1 norm of quantum coherence of an optical cat state on its amplitude. The red solid and blue dashed curves correspond the results in the 16-dimensional and 12-dimensional Hilbert space, respectively.