Fig. 1: Experiment Overview.

a Schematic of the experimental setup. The Laser Diode (LD) emits a continuous-wave laser, which is split into two parts by a Beam Splitter(BS). One is for quantum state preparation, and the other is for Local Oscillator (LO) for homodyne detection. In the signal path, an Intensity Modulator (IM) is used for pulse curving and intensity modulation, and a Phase Modulator (PM) is used for phase modulation. The optical signal is then attenuated to single-photon energy level by an attenuator (ATT). The final quantum states after modulation are in QPSK or QAM-16 format. In the LO path, a PM is deployed for basis choosing for the homodyne detection. The signal states and the LO are mixed on a balanced BS, and the photocurrent of two photodiodes (PD) are subtracted and further amplified. Finally, a data acquisition (DAQ) device samples the signal and obtain the data for analysis. b, c Constellation diagram for QPSK modulation and QAM-16 modulation, respectively. The blue circles represent the quantum states to be prepared by the transmitter. The circle with red centre represents the state used when the randomness generation round is chosen, and all the states are used for the testing rounds. The black dashed lines represent the two measurement bases in our protocol. For the convenience of illustration, we shift the phase of the states and measurements by π/4 comparing to the descriptions in the main text. This will not affect either the security analysis or the experimental results. d, e Homodyne detector characterisation. d Power spectrum of the homodyne detector from DC to 120 MHz. The 3 dB bandwidth is ~72 MHz. e Noise variance for different LO powers. A clearance of 16.94 dB is obtained with 10 mW LO input.