Fig. 1. Finite-size and LLO CV-QKD optical layout. The signal light generated by Alice’s laser 1 is transmitted to the in-phase and quadrature modulator (IQM). Then, the modulated coherent state is divided into two parts by a beam splitter (BS). One part of the light is transmitted to the automatic bias controller (ABC), while the other part is transmitted to the variable optical attenuator (VOA). After intensity adjustment by VOA, the light is transmitted into the optical fiber channel. We introduced a piezoelectric transducer (PZT) in the optical fiber channel to simulate the field-test environment. Then, the coherent state enters the polarization controller (PC) for polarization adjustment. Finally, the quantum signal outputs from the PC and the local oscillator (LO) of Bob’s laser 2 are simultaneously input into the integrated coherent receiver (ICR) for coherent detection.

Fig. 2. LLO CV-QKD system. (a) Experimental structure. (b) Complex frequency spectrum (CFS) of the signal modulated by Alice. (c) CFS of the signal detected by Bob. (d) CFS of the signal recovered by Bob. (e) Complex power spectrum (CPS) of the signal modulated by Alice. (f) CPS of the signal detected by Bob. (f) CFS of the signal recovered by Bob. (g) CPS of the signal recovered by Bob.

Fig. 3. Time-variant parameters measured in the experiment. (a) Frequency deviation. The mean frequency deviation is 89.05 MHz/s. It is mainly caused by two lasers with the unlocked frequency, which is similar to the situation encountered during a field-test experiment where two lasers are difficult to synchronize. (b) Phase change. The mean phase change is 3.036 Mrad/s. It is mainly caused by the vibration of PZT, which is comparable to the scenario in the field-test experiment where vehicles pass through the optical fiber.

Fig. 4. Histogram of recovered signal. The signal processed by time-variant parameter digital signal processing demonstrates a Gaussian distribution.

Fig. 5. Phase power spectrum of the interference signal. The interference-to-noise ratio (INR) of the interference signal is 42.92 dB.

Fig. 6. Excess noise with time-variant estimation and time-invariant estimation. The color of the scatter points indicates the magnitude of the excess noise. In the time-variant estimation, the excess noise is represented by the blue scale on the left side of the figure, with an average value of ε=0.0275  SNU. Similarly, in the time-invariant estimation, the excess noise is depicted by the red scale on the right side of the figure, with an average value of 7.9428 SNU.

Fig. 7. SKR of LLO CV-QKD system. The red line is the theoretical SKR in the finite-size case, where the three points correspond to the results achieved in three experiments. The blue line is the theoretical SKR in the asymptotic case, where the single point on the blue line corresponds to the result in one experiment.