Fig. 1. Representation of the vacuum state and coherent state in phase space, where the diameter of the circles represents the magnitude of the optical field noise, and α signifies the amplitude of the coherent state, while θ indicates the phase of the coherent state. (a) Noise fluctuation of vacuum state; (b) noise fluctuation of coherent state

Fig. 2. Representation of single-mode squeezed vacuum state in phase space, where the diameter of the circles represents the magnitude of the optical field noise fluctuations. (a) The vacuum state is squeezed in the amplitude direction; (b) the vacuum state is squeezed in the phase direction

Fig. 3. Two amplitude-squeezed beams generate a two-mode entangled state (BS: 50∶50 beam splitter)

Fig. 4. Balanced homodyne detection (LO: local oscillator light; BS: 50∶50 beam splitter; D: photodetectors; S: subtractor)

Fig. 5. Intensity difference detection ( CL: coherent light; BS: 50∶50 beam splitter; a^andb^: two optical fields for measuring intensity difference; FM: folding mirror; M: mirror; D: photodetector; S: subtractor)

Fig. 6. Network of beam splitters coupled multiple single-mode squeezed states to generate N-mode entangled states

Fig. 7. Spatial multimode of Gaussian profile

Fig. 8. Generating large-scale entangled states based on time-delay

Fig. 9. Generating large-scale entangled states based on frequency multiplexing