Efficient frame synchronization using a weak coherent state for continuous-variable quantum key distribution

Frame synchronization is a crucial step in quantum key distribution (QKD) and a prerequisite for secure key distillation. Due to the extremely low signal-to-noise ratio (SNR) and fast phase drift in the continuous-variable QKD system, efficient frame synchronization is highly demanded. In this paper, a frame-synchronization scheme based on weak coherent states is proposed. This scheme uses a train of coherent-state pulses encoded by a Zadoff-Chu sequence to achieve frame synchronization. The synchronization performance is analyzed under different transmission distances, transmit powers, frequency offsets, and phase drifts through Monte Carlo simulation. Its performance is also compared with other synchronization sequences, confirming its noise-tolerance capability. An optical experiment is conducted to verify the feasibility of the synchronization scheme under low SNR (as low as $-20$ dB), and the applicable SNR range can be further reduced by increasing the sequence length. Due to its efficiency and noise tolerance, this scheme can provide technical support for weak-coherent-state-based QKD and future quantum network construction.

Figure 1

The flow diagram for the GG02 protocol. (1) Quantum signal modulation. (2) Quantum signal transmission. (3) Quantum signal reception. (4) Parameter estimation. (5) Data processing.

Figure 2

The time domain and complex domain of the ZC sequence. (a) Without noise. The root index is 1, and the length of the ZC sequence is 1000. (b) With quantum noise. The root index is 1. The length of the ZC sequence is 1000.

Figure 3

The diagram of the frame-synchronization scheme based on the ZC sequence. $z_r\left[n\right]$ represents the ZC sequence. $g\left[n\right]$ represents the Gaussian data sequence. $p\left[n\right]$ represents the pilot sequence. $y\left[n\right]=[z_r{\left[n\right]}^{\prime },g{\left[n\right]}^{\prime }]$ and expressions for $z_r{\left[n\right]}^{\prime }$ and $g{\left[n\right]}^{\prime }$ are shown in Eqs. (4) and (5).

Figure 4

Self-correlation and cross-correlation properties of different sequences. (a) Zadoff-Chu sequence. (b) Gaussian sequence. (c) Binomial distribution sequence.

Figure 5

Synchronization performance with ZC sequences of different lengths. (a) Synchronization performance of the ZC sequence for different lengths. (b) The length of the ZC sequence needed for successful synchronization. When synchronization is completed successfully, the ordinate value, synchronization success, is 1, while the value is 0 when synchronization fails.

Figure 6

Comparison of synchronization success rates with ZC sequences of different lengths.

Figure 7

Diagram of average secret key rate with different receivers' SNRs.

Figure 8

Synchronization performance of the fixed-length ZC sequence under different frequency offsets and phase drifts. (a) Synchronization performance under different frequency offsets. (b) Synchronization performance under different phase drifts. When synchronization succeeds, the value of the ordinate is 1, while the value is 0 when synchronization fails.

Figure 9

Diagram of the experimental device based on frame synchronization with weak coherent states in the LLO CV-QKD system. (a) The wave form of the synchronization frame. (b) The complex domain of the synchronization frame. (c) The value of the $x$ quadrature. (d) The value of the $p$ quadrature.

Figure 10

The experimental results with different SNRs. (a) Mean value of SNR is $-3.97$ dB (length of the ZC sequence is 1000). (b) Mean value of SNR is $-8.24$ dB (length of the ZC sequence is 1000). (c) Mean value of SNR is $-15.57$ dB (length of the ZC sequence is 1000). (d) Mean value of SNR is $-19.82$ dB (length of the ZC sequence is 8000).